NPB Model for Birth Weight
Sheena Martenies
02/10/2021
#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------
#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.0.6 ✓ dplyr 1.0.4
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(haven)
library(readxl)
library(mmpack)
#' For ggplots
simple_theme <- theme(
#aspect.ratio = 1,
text = element_text(family="Calibri",size = 12, color = 'black'),
panel.spacing.y = unit(0,"cm"),
panel.spacing.x = unit(0.25, "lines"),
panel.grid.minor = element_line(color = "transparent"),
panel.grid.major = element_line(color = "transparent"),
panel.border=element_rect(fill = NA),
panel.background=element_blank(),
axis.ticks = element_line(colour = "black"),
axis.text = element_text(color = "black", size=10),
# legend.position = c(0.1,0.1),
plot.margin=grid::unit(c(0,0,0,0), "mm"),
legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation
set.seed(123)1 Sensitivty Analysis
In this version of the analysis, we are excluding race/ethnicity because the DAG may indicate the race/ethnicty are on the causal path (modifers, not confounders)
1.1 Exposure data
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072 51.81487 6.006276 43.30893
## [2,] 6.598608 50.05090 58.32885 7.281109 48.36432
## [3,] 7.454146 48.57052 58.01924 17.205991 31.67281
## [4,] 6.671239 50.06429 61.35590 6.842898 45.00359
## [5,] 7.122537 50.14275 59.28421 3.357792 28.16745
## [6,] 7.637453 47.03125 55.32825 10.743612 45.87564
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] 10128.4962 2827.538 729.2371 4829.780
## [2,] 10749.0359 1576.420 5239.2211 4417.792
## [3,] 9048.6468 3350.303 2992.2968 5211.871
## [4,] 4223.3434 3364.954 6998.1286 8921.318
## [5,] 858.7283 2923.811 3427.2247 7006.042
## [6,] 15603.9800 3364.200 3166.5395 4484.960
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] 7968.654 29116.58 1749.1256 275.2480 155.7767
## [2,] 3780.951 51044.30 7354.5310 279.6435 226.8038
## [3,] 7423.232 36079.21 4887.2996 221.0414 157.6974
## [4,] 9636.816 42235.78 3752.6399 203.8812 142.5368
## [5,] 6806.912 29145.98 729.7784 194.1983 101.0046
## [6,] 5265.285 43921.85 5870.6867 174.3361 120.3281
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 14.377133 37.32935 31.784946 11.529628
## [2,] 8.905404 67.03932 15.290231 4.908306
## [3,] 7.636888 46.78194 6.891702 4.564963
## [4,] 2.850212 21.95270 2.725915 5.623583
## [5,] 5.435988 22.49834 12.919186 5.234103
## [6,] 5.035971 47.15500 3.842365 10.000000
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 26.114650 12.010919 90.33703
## [2,] 8.500401 18.123496 30.44025
## [3,] 0.000000 6.307978 26.63305
## [4,] 1.350621 9.292274 32.68648
## [5,] 6.307385 2.115768 73.60772
## [6,] 5.121799 25.171768 23.08698Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 0.391784015 0.006083605 0.09741867 -0.2054297
## mean_o3 0.006083605 9.383489039 11.72688428 -0.4158151
## mean_temp 0.097418667 11.726884276 20.59970005 0.4425544
## pct_tree_cover -0.205429726 -0.415815089 0.44255440 9.7193077
## pct_impervious 0.508898445 -1.674151031 3.35723856 5.8719893
## mean_aadt_intensity -182.234953786 474.627052967 2674.12174077 8431.6446632
## dist_m_tri -255.176839682 444.286548683 -627.63132786 -73.1423054
## dist_m_npl -289.002141382 539.849185829 -165.00509261 434.4654007
## dist_m_waste_site -275.262105884 261.902915064 58.19389166 1933.8647304
## dist_m_major_emit 71.096593638 577.257325397 138.98687089 265.4284518
## dist_m_cafo -1291.237441927 -35.275020052 237.89751842 10170.6234275
## dist_m_mine_well -339.250592215 -375.434990683 -202.34883778 3136.3680766
## cvd_rate_adj 3.871688575 0.939328342 7.31791796 -24.8232924
## res_rate_adj 2.356328835 -0.181515705 7.98167422 -3.5331376
## violent_crime_rate 0.232839920 0.577648302 1.07794996 -4.0583754
## property_crime_rate 2.001989749 -2.773092354 6.06649992 -22.6429724
## pct_less_hs 1.132232861 0.637361326 0.69410116 -7.5753471
## pct_unemp 0.100439902 0.288530482 0.25729682 -0.3330523
## pct_limited_eng 0.432516169 0.295617023 0.05811301 -2.8349116
## pct_hh_pov 0.731824476 -0.606648513 0.73475917 0.3805472
## pct_poc 1.632059580 1.202932299 -0.90133106 -19.4091792
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.5088984 -182.2350 -255.17684
## mean_o3 -1.6741510 474.6271 444.28655
## mean_temp 3.3572386 2674.1217 -627.63133
## pct_tree_cover 5.8719893 8431.6447 -73.14231
## pct_impervious 176.8316214 55459.6063 -15279.44024
## mean_aadt_intensity 55459.6063235 67283287.0201 -1315386.69307
## dist_m_tri -15279.4402428 -1315386.6931 6558190.20296
## dist_m_npl -7729.3843793 1683196.0799 4282727.94125
## dist_m_waste_site -4662.9983638 2039577.9230 2441267.84540
## dist_m_major_emit 2627.0270993 2477155.3406 1433153.16531
## dist_m_cafo 16586.9964129 15462371.9832 3431065.70215
## dist_m_mine_well 706.6674650 2073244.5987 995872.11873
## cvd_rate_adj 230.4542985 20477.4374 -49347.60273
## res_rate_adj 176.8108084 33055.3733 -31870.98664
## violent_crime_rate 26.6945028 5736.5627 -1014.08753
## property_crime_rate 118.0737725 22077.3894 -5365.69285
## pct_less_hs 56.8383947 -4056.6889 -12372.14262
## pct_unemp 25.9434246 6003.3343 -2527.22451
## pct_limited_eng 41.9919053 2620.6198 -5408.86434
## pct_hh_pov 82.2198624 17850.1649 -8842.76408
## pct_poc 88.3560154 4526.2710 -18049.42332
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -289.0021 -275.26211 71.09659
## mean_o3 539.8492 261.90292 577.25733
## mean_temp -165.0051 58.19389 138.98687
## pct_tree_cover 434.4654 1933.86473 265.42845
## pct_impervious -7729.3844 -4662.99836 2627.02710
## mean_aadt_intensity 1683196.0799 2039577.92299 2477155.34057
## dist_m_tri 4282727.9413 2441267.84540 1433153.16531
## dist_m_npl 11125411.7474 4193498.05859 6948817.25739
## dist_m_waste_site 4193498.0586 5344101.75397 1395277.06805
## dist_m_major_emit 6948817.2574 1395277.06805 10114549.72263
## dist_m_cafo 5416531.1320 5586018.82514 -2993791.05377
## dist_m_mine_well 256924.3029 1375784.78556 -1810174.74785
## cvd_rate_adj -30921.0390 -43119.57852 16272.40152
## res_rate_adj -19393.1304 -32402.84395 -1320.21297
## violent_crime_rate -672.9264 -3702.61118 -360.49700
## property_crime_rate -18283.4264 -22350.30055 -24007.42305
## pct_less_hs -6760.5337 -11422.49855 8866.74917
## pct_unemp 2195.0515 -1476.40942 5212.74830
## pct_limited_eng 498.0033 -4277.81339 9367.28435
## pct_hh_pov -1135.3843 -7599.74324 8682.26135
## pct_poc -1456.8941 -8602.85207 22698.24353
## dist_m_cafo dist_m_mine_well cvd_rate_adj
## mean_pm -1291.23744 -339.2506 3.8716886
## mean_o3 -35.27502 -375.4350 0.9393283
## mean_temp 237.89752 -202.3488 7.3179180
## pct_tree_cover 10170.62343 3136.3681 -24.8232924
## pct_impervious 16586.99641 706.6675 230.4542985
## mean_aadt_intensity 15462371.98316 2073244.5987 20477.4373759
## dist_m_tri 3431065.70215 995872.1187 -49347.6027339
## dist_m_npl 5416531.13199 256924.3029 -30921.0389720
## dist_m_waste_site 5586018.82514 1375784.7856 -43119.5785165
## dist_m_major_emit -2993791.05377 -1810174.7478 16272.4015197
## dist_m_cafo 46324000.89481 9345575.3772 -46645.9665229
## dist_m_mine_well 9345575.37722 4430024.9964 -39046.5984701
## cvd_rate_adj -46645.96652 -39046.5985 2039.8569530
## res_rate_adj -13772.40263 -16322.5110 1289.5661935
## violent_crime_rate 722.31907 -2032.3464 135.9487143
## property_crime_rate -15833.92381 -4272.3829 343.9364726
## pct_less_hs -26060.83378 -10037.6577 328.3044447
## pct_unemp -1030.96916 -2827.2369 105.0153846
## pct_limited_eng -7089.15821 -4814.6687 183.5853966
## pct_hh_pov -855.38016 -5030.4055 266.1004715
## pct_poc -44526.37107 -24974.3303 618.2817294
## res_rate_adj violent_crime_rate property_crime_rate
## mean_pm 2.3563288 0.2328399 2.001990
## mean_o3 -0.1815157 0.5776483 -2.773092
## mean_temp 7.9816742 1.0779500 6.066500
## pct_tree_cover -3.5331376 -4.0583754 -22.642972
## pct_impervious 176.8108084 26.6945028 118.073773
## mean_aadt_intensity 33055.3733277 5736.5627383 22077.389365
## dist_m_tri -31870.9866403 -1014.0875345 -5365.692846
## dist_m_npl -19393.1304345 -672.9263612 -18283.426420
## dist_m_waste_site -32402.8439544 -3702.6111771 -22350.300554
## dist_m_major_emit -1320.2129699 -360.4970006 -24007.423046
## dist_m_cafo -13772.4026269 722.3190727 -15833.923813
## dist_m_mine_well -16322.5110008 -2032.3464340 -4272.382880
## cvd_rate_adj 1289.5661935 135.9487143 343.936473
## res_rate_adj 1091.1856742 104.4979610 333.780710
## violent_crime_rate 104.4979610 40.1175363 160.725724
## property_crime_rate 333.7807097 160.7257236 1295.004010
## pct_less_hs 197.8827546 22.5579950 -3.138375
## pct_unemp 72.3576933 11.3130282 1.362247
## pct_limited_eng 104.0524036 12.7978322 -14.963510
## pct_hh_pov 201.6582659 29.1947400 64.236239
## pct_poc 297.8399442 46.4013012 -44.321973
## pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## mean_pm 1.1322329 0.1004399 0.43251617 0.7318245
## mean_o3 0.6373613 0.2885305 0.29561702 -0.6066485
## mean_temp 0.6941012 0.2572968 0.05811301 0.7347592
## pct_tree_cover -7.5753471 -0.3330523 -2.83491161 0.3805472
## pct_impervious 56.8383947 25.9434246 41.99190527 82.2198624
## mean_aadt_intensity -4056.6889048 6003.3343312 2620.61975287 17850.1649192
## dist_m_tri -12372.1426191 -2527.2245090 -5408.86433682 -8842.7640785
## dist_m_npl -6760.5337115 2195.0514738 498.00334199 -1135.3843390
## dist_m_waste_site -11422.4985495 -1476.4094188 -4277.81339346 -7599.7432386
## dist_m_major_emit 8866.7491706 5212.7483023 9367.28434718 8682.2613524
## dist_m_cafo -26060.8337755 -1030.9691591 -7089.15821141 -855.3801591
## dist_m_mine_well -10037.6576614 -2827.2368665 -4814.66874000 -5030.4055237
## cvd_rate_adj 328.3044447 105.0153846 183.58539661 266.1004715
## res_rate_adj 197.8827546 72.3576933 104.05240356 201.6582659
## violent_crime_rate 22.5579950 11.3130282 12.79783224 29.1947400
## property_crime_rate -3.1383751 1.3622468 -14.96351049 64.2362387
## pct_less_hs 162.1681017 39.4206217 85.19100137 100.9072175
## pct_unemp 39.4206217 24.6546969 25.21727694 36.9693212
## pct_limited_eng 85.1910014 25.2172769 68.65329426 67.2758215
## pct_hh_pov 100.9072175 36.9693212 67.27582153 119.7157808
## pct_poc 238.8801445 72.7999599 142.19618383 155.4992975
## pct_poc
## mean_pm 1.6320596
## mean_o3 1.2029323
## mean_temp -0.9013311
## pct_tree_cover -19.4091792
## pct_impervious 88.3560154
## mean_aadt_intensity 4526.2710457
## dist_m_tri -18049.4233248
## dist_m_npl -1456.8941447
## dist_m_waste_site -8602.8520680
## dist_m_major_emit 22698.2435288
## dist_m_cafo -44526.3710716
## dist_m_mine_well -24974.3303024
## cvd_rate_adj 618.2817294
## res_rate_adj 297.8399442
## violent_crime_rate 46.4013012
## property_crime_rate -44.3219731
## pct_less_hs 238.8801445
## pct_unemp 72.7999599
## pct_limited_eng 142.1961838
## pct_hh_pov 155.4992975
## pct_poc 524.7591044ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 1.60876944 -0.2502907 -0.1690421 -0.08261827 0.2084897
## [2,] -1.40186806 0.6834152 1.2661699 0.32629926 0.5886571
## [3,] -0.03503482 0.2001460 1.1979551 3.50981981 -0.6665506
## [4,] -1.28583023 0.6877893 1.9331141 0.18573791 0.3359288
## [5,] -0.56482237 0.7133998 1.4766616 -0.93215008 -0.9301550
## [6,] 0.25782234 -0.3023500 0.6050531 1.43693690 0.4015075
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] -0.02626143 -0.4008664 -1.44212141 -0.172775897
## [2,] 0.04938980 -0.8894134 -0.08999604 -0.350992130
## [3,] -0.15790801 -0.1967327 -0.76363997 -0.007492447
## [4,] -0.74617032 -0.1910117 0.43733697 1.597126043
## [5,] -1.15635722 -0.3632728 -0.63324550 0.768623456
## [6,] 0.64126566 -0.1913062 -0.71140077 -0.321936759
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] -0.1090638 -1.1354079 -0.7748959 0.6917151 -0.2847192
## [2,] -1.4258114 2.0863310 1.8883051 0.7890362 1.8654606
## [3,] -0.2805619 -0.1124210 0.7160914 -0.5084805 -0.2265752
## [4,] 0.4154599 0.7921355 0.1769998 -0.8884275 -0.6855261
## [5,] -0.4743524 -1.1310891 -1.2592010 -1.1028189 -1.9428184
## [6,] -0.9590895 1.0398621 1.1833114 -1.5425892 -1.3578439
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 0.2444833 -0.5008789 1.20091488 0.36793456
## [2,] -0.6194047 0.3247153 -0.09436047 -0.96557105
## [3,] -0.8196807 -0.2382061 -0.75386917 -1.03471894
## [4,] -1.5754111 -0.9281724 -1.08099463 -0.82151747
## [5,] -1.1671633 -0.9130100 -0.28055077 -0.89995692
## [6,] -1.2303189 -0.2278392 -0.99332353 0.05987409
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 2.15383825 -0.3020187 1.5727240
## [2,] 0.02798425 0.2566428 -1.0419857
## [3,] -0.99792447 -0.8232412 -1.2081839
## [4,] -0.83491873 -0.5504902 -0.9439299
## [5,] -0.23668961 -1.2063898 0.8424295
## [6,] -0.37977738 0.9008223 -1.3629822Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 1.000000000 0.003172893 0.034291650 -0.105274276
## mean_o3 0.003172893 1.000000000 0.843470729 -0.043541201
## mean_temp 0.034291650 0.843470729 1.000000000 0.031276529
## pct_tree_cover -0.105274276 -0.043541201 0.031276529 1.000000000
## pct_impervious 0.061140333 -0.041099117 0.055625226 0.141640558
## mean_aadt_intensity -0.035493982 0.018889337 0.071828554 0.329716765
## dist_m_tri -0.159193706 0.056635532 -0.053998558 -0.009161339
## dist_m_npl -0.138426634 0.052836279 -0.010899557 0.041781063
## dist_m_waste_site -0.190232937 0.036984589 0.005546380 0.268331135
## dist_m_major_emit 0.035715124 0.059253499 0.009628753 0.026770503
## dist_m_cafo -0.303095664 -0.001691929 0.007701165 0.479321466
## dist_m_mine_well -0.257510042 -0.058230361 -0.021182010 0.477976199
## cvd_rate_adj 0.136954783 0.006789463 0.035699097 -0.176295758
## res_rate_adj 0.113962827 -0.001793836 0.053237079 -0.034307854
## violent_crime_rate 0.058730941 0.029772424 0.037497389 -0.205526308
## property_crime_rate 0.088879773 -0.025156291 0.037142591 -0.201827442
## pct_less_hs 0.142046220 0.016338825 0.012009076 -0.190810449
## pct_unemp 0.032317153 0.018969666 0.011417056 -0.021515177
## pct_limited_eng 0.083396591 0.011647067 0.001545298 -0.109746623
## pct_hh_pov 0.106858205 -0.018100029 0.014795814 0.011156172
## pct_poc 0.113823690 0.017142692 -0.008669098 -0.271775006
## pct_impervious mean_aadt_intensity dist_m_tri dist_m_npl
## mean_pm 0.06114033 -0.03549398 -0.159193706 -0.13842663
## mean_o3 -0.04109912 0.01888934 0.056635532 0.05283628
## mean_temp 0.05562523 0.07182855 -0.053998558 -0.01089956
## pct_tree_cover 0.14164056 0.32971677 -0.009161339 0.04178106
## pct_impervious 1.00000000 0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity 0.50844411 1.00000000 -0.062619247 0.06152095
## dist_m_tri -0.44867872 -0.06261925 1.000000000 0.50138396
## dist_m_npl -0.17426369 0.06152095 0.501383960 1.00000000
## dist_m_waste_site -0.15168685 0.10755964 0.412369055 0.54385239
## dist_m_major_emit 0.06211712 0.09495686 0.175965418 0.65505772
## dist_m_cafo 0.18326720 0.27696155 0.196849357 0.23859436
## dist_m_mine_well 0.02524829 0.12008641 0.184760224 0.03659688
## cvd_rate_adj 0.38371166 0.05527416 -0.426652406 -0.20525615
## res_rate_adj 0.40251263 0.12199419 -0.376750794 -0.17601130
## violent_crime_rate 0.31693831 0.11041575 -0.062519618 -0.03185242
## property_crime_rate 0.24673907 0.07479259 -0.058223492 -0.15232247
## pct_less_hs 0.33564418 -0.03883608 -0.379376300 -0.15916230
## pct_unemp 0.39291400 0.14739715 -0.198747643 0.13253691
## pct_limited_eng 0.38111402 0.03855846 -0.254907958 0.01801953
## pct_hh_pov 0.56509450 0.19888999 -0.315587892 -0.03111065
## pct_poc 0.29005220 0.02408835 -0.307674381 -0.01906733
## dist_m_waste_site dist_m_major_emit dist_m_cafo
## mean_pm -0.19023294 0.035715124 -0.303095664
## mean_o3 0.03698459 0.059253499 -0.001691929
## mean_temp 0.00554638 0.009628753 0.007701165
## pct_tree_cover 0.26833114 0.026770503 0.479321466
## pct_impervious -0.15168685 0.062117120 0.183267205
## mean_aadt_intensity 0.10755964 0.094956864 0.276961553
## dist_m_tri 0.41236906 0.175965418 0.196849357
## dist_m_npl 0.54385239 0.655057717 0.238594356
## dist_m_waste_site 1.00000000 0.189779728 0.355027509
## dist_m_major_emit 0.18977973 1.000000000 -0.138307324
## dist_m_cafo 0.35502751 -0.138307324 1.000000000
## dist_m_mine_well 0.28275484 -0.270423318 0.652378929
## cvd_rate_adj -0.41298787 0.113286594 -0.151743889
## res_rate_adj -0.42432287 -0.012566704 -0.061257230
## violent_crime_rate -0.25287368 -0.017896218 0.016755559
## property_crime_rate -0.26866460 -0.209766780 -0.064647236
## pct_less_hs -0.38800832 0.218931589 -0.300678627
## pct_unemp -0.12862329 0.330098571 -0.030506530
## pct_limited_eng -0.22333346 0.355475551 -0.125707430
## pct_hh_pov -0.30045944 0.249507656 -0.011486308
## pct_poc -0.16245202 0.311558055 -0.285584268
## dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.25751004 0.136954783 0.113962827
## mean_o3 -0.05823036 0.006789463 -0.001793836
## mean_temp -0.02118201 0.035699097 0.053237079
## pct_tree_cover 0.47797620 -0.176295758 -0.034307854
## pct_impervious 0.02524829 0.383711656 0.402512635
## mean_aadt_intensity 0.12008641 0.055274160 0.121994187
## dist_m_tri 0.18476022 -0.426652406 -0.376750794
## dist_m_npl 0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site 0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit -0.27042332 0.113286594 -0.012566704
## dist_m_cafo 0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well 1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj -0.41075254 1.000000000 0.864359590
## res_rate_adj -0.23476565 0.864359590 1.000000000
## violent_crime_rate -0.15245003 0.475234675 0.499449246
## property_crime_rate -0.05640681 0.211613232 0.280786581
## pct_less_hs -0.37449548 0.570813439 0.470409304
## pct_unemp -0.27052616 0.468277441 0.441149256
## pct_limited_eng -0.27607853 0.490577454 0.380164971
## pct_hh_pov -0.21843600 0.538480631 0.557944498
## pct_poc -0.51797735 0.597594464 0.393598671
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.05873094 0.088879773 0.14204622
## mean_o3 0.02977242 -0.025156291 0.01633882
## mean_temp 0.03749739 0.037142591 0.01200908
## pct_tree_cover -0.20552631 -0.201827442 -0.19081045
## pct_impervious 0.31693831 0.246739067 0.33564418
## mean_aadt_intensity 0.11041575 0.074792588 -0.03883608
## dist_m_tri -0.06251962 -0.058223492 -0.37937630
## dist_m_npl -0.03185242 -0.152322474 -0.15916230
## dist_m_waste_site -0.25287368 -0.268664603 -0.38800832
## dist_m_major_emit -0.01789622 -0.209766780 0.21893159
## dist_m_cafo 0.01675556 -0.064647236 -0.30067863
## dist_m_mine_well -0.15245003 -0.056406808 -0.37449548
## cvd_rate_adj 0.47523468 0.211613232 0.57081344
## res_rate_adj 0.49944925 0.280786581 0.47040930
## violent_crime_rate 1.00000000 0.705151942 0.27967307
## property_crime_rate 0.70515194 1.000000000 -0.00684836
## pct_less_hs 0.27967307 -0.006848360 1.00000000
## pct_unemp 0.35971778 0.007623781 0.62343462
## pct_limited_eng 0.24385889 -0.050184228 0.80738433
## pct_hh_pov 0.42127121 0.163143151 0.72420883
## pct_poc 0.31980337 -0.053765481 0.81887450
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.032317153 0.083396591 0.10685820 0.113823690
## mean_o3 0.018969666 0.011647067 -0.01810003 0.017142692
## mean_temp 0.011417056 0.001545298 0.01479581 -0.008669098
## pct_tree_cover -0.021515177 -0.109746623 0.01115617 -0.271775006
## pct_impervious 0.392914001 0.381114020 0.56509450 0.290052202
## mean_aadt_intensity 0.147397153 0.038558463 0.19888999 0.024088345
## dist_m_tri -0.198747643 -0.254907958 -0.31558789 -0.307674381
## dist_m_npl 0.132536906 0.018019533 -0.03111065 -0.019067333
## dist_m_waste_site -0.128623290 -0.223333456 -0.30045944 -0.162452016
## dist_m_major_emit 0.330098571 0.355475551 0.24950766 0.311558055
## dist_m_cafo -0.030506530 -0.125707430 -0.01148631 -0.285584268
## dist_m_mine_well -0.270526163 -0.276078529 -0.21843600 -0.517977353
## cvd_rate_adj 0.468277441 0.490577454 0.53848063 0.597594464
## res_rate_adj 0.441149256 0.380164971 0.55794450 0.393598671
## violent_crime_rate 0.359717785 0.243858891 0.42127121 0.319803374
## property_crime_rate 0.007623781 -0.050184228 0.16314315 -0.053765481
## pct_less_hs 0.623434625 0.807384330 0.72420883 0.818874497
## pct_unemp 1.000000000 0.612939575 0.68048090 0.640031449
## pct_limited_eng 0.612939575 1.000000000 0.74208323 0.749164620
## pct_hh_pov 0.680480902 0.742083231 1.00000000 0.620401357
## pct_poc 0.640031449 0.749164620 0.62040136 1.000000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.2 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
W <- select(hs_data2,
lat, lon, lat_lon_int,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w) %>%
as.matrix()
head(W)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.79402 -104.8133 -4170.944 0 0 1 0 0
## [2,] 39.62671 -104.9927 -4160.517 0 0 1 0 0
## [3,] 39.74934 -104.9129 -4170.219 0 0 0 0 0
## [4,] 39.68397 -104.8933 -4162.583 0 0 1 0 0
## [5,] 39.79134 -104.7669 -4168.814 0 0 0 1 0
## [6,] 39.68050 -104.9451 -4164.274 0 0 1 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1
## [3,] 0 0 0 0 0 1
## [4,] 0 0 1 0 0 1
## [5,] 0 0 1 0 0 1
## [6,] 0 0 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 19 0 1
## [2,] 0 0 0 36 0 0
## [3,] 0 0 0 34 0 0
## [4,] 0 0 0 28 0 0
## [5,] 0 0 0 30 0 0
## [6,] 0 0 0 22 0 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 29 0 0 40.57143
## [2,] 19 2 1 35.85714
## [3,] 19 1 0 40.42857
## [4,] 20 0 0 36.28571
## [5,] 15 0 1 38.42857
## [6,] 17 1 0 40.71429Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:17], W.s[,4],
W[,19:20], W.s[,5:6],
W[,23], W.s[,7])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "" ""colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 0.9587536 0.5410850 -0.5821980 0 0 1 0 0
## [2,] -1.5498523 -1.6236392 0.6519093 0 0 1 0 0
## [3,] 0.2887793 -0.6606299 -0.4964164 0 0 0 0 0
## [4,] -0.6913627 -0.4239607 0.4073829 0 0 1 0 0
## [5,] 0.9185421 1.1019032 -0.3300513 0 0 0 1 0
## [6,] -0.7433125 -1.0489343 0.2071583 0 0 1 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1
## [3,] 0 0 0 0 0 1
## [4,] 0 0 1 0 0 1
## [5,] 0 0 1 0 0 1
## [6,] 0 0 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 -1.39815187 0 1
## [2,] 0 0 0 1.35109608 0 0
## [3,] 0 0 0 1.02765515 0 0
## [4,] 0 0 0 0.05733234 0 0
## [5,] 0 0 0 0.38077328 0 0
## [6,] 0 0 0 -0.91299047 0 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 3.3147856 -1.2832098 0 0.7037686
## [2,] 0.1179652 -0.6860171 1 -1.9146645
## [3,] 0.1179652 -0.9846134 0 0.6244221
## [4,] 0.4376472 -1.2832098 0 -1.6766251
## [5,] -1.1607630 -1.2832098 1 -0.4864283
## [6,] -0.5213989 -0.9846134 0 0.7831150summary(W.scaled)## lat lon lat_lon_int ed_no_hs
## Min. :-2.45418 Min. :-2.5043 Min. :-3.48430 Min. :0.0000
## 1st Qu.:-0.62577 1st Qu.:-0.5848 1st Qu.:-0.48738 1st Qu.:0.0000
## Median : 0.03151 Median : 0.1214 Median : 0.02121 Median :0.0000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000 Mean :0.1527
## 3rd Qu.: 0.42402 3rd Qu.: 0.6654 3rd Qu.: 0.60627 3rd Qu.:0.0000
## Max. : 4.00304 Max. : 4.5531 Max. : 2.60273 Max. :1.0000
## ed_hs ed_aa ed_4yr low_bmi
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.1851 Mean :0.2319 Mean :0.2185 Mean :0.03344
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## ovwt_bmi obese_bmi concep_spring concep_summer
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.262 Mean :0.1996 Mean :0.2497 Mean :0.2408
## 3rd Qu.:1.000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_fall concep_2010 concep_2011 concep_2012
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2709 Mean :0.1616 Mean :0.3021 Mean :0.2932
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_2013 maternal_age any_smoker smokeSH
## Min. :0.0000 Min. :-1.88331 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:-0.91299 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median : 0.05733 Median :0.00000 Median :0.0000
## Mean :0.2419 Mean : 0.00000 Mean :0.08696 Mean :0.2575
## 3rd Qu.:0.0000 3rd Qu.: 0.70421 3rd Qu.:0.00000 3rd Qu.:1.0000
## Max. :1.0000 Max. : 2.64486 Max. :1.00000 Max. :1.0000
## mean_cpss mean_epsd male gest_age_w
## Min. :-5.9560 Min. :-1.2832 Min. :0.0000 Min. :-7.7070
## 1st Qu.:-0.5214 1st Qu.:-0.7855 1st Qu.:0.0000 1st Qu.:-0.3277
## Median : 0.0114 Median :-0.1884 Median :1.0000 Median : 0.1483
## Mean : 0.0000 Mean : 0.0000 Mean :0.5117 Mean : 0.0000
## 3rd Qu.: 0.5442 3rd Qu.: 0.6079 3rd Qu.:1.0000 3rd Qu.: 0.6244
## Max. : 4.5935 Max. : 6.0324 Max. :1.0000 Max. : 2.9255Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int ed_no_hs
## lat 1.000000000 -0.25261855699 -0.926170284 0.0058668471
## lon -0.252618557 1.00000000000 0.598841550 0.0173291290
## lat_lon_int -0.926170284 0.59884155012 1.000000000 0.0019047436
## ed_no_hs 0.005866847 0.01732912905 0.001904744 0.1295488931
## ed_hs -0.013065279 0.04117136599 0.026869409 -0.0282962056
## ed_aa -0.007178943 0.04676104709 0.024182422 -0.0354554865
## ed_4yr 0.002235236 -0.00766878563 -0.004860779 -0.0334099777
## low_bmi -0.002977458 -0.00003551643 0.002453115 -0.0039977007
## ovwt_bmi 0.020588007 0.00512460048 -0.015060264 0.0045849757
## obese_bmi 0.016566934 0.00976713009 -0.009896473 0.0063181836
## concep_spring 0.014329290 -0.00046075172 -0.012039363 -0.0002364031
## concep_summer -0.014031905 -0.00711327850 0.008844405 -0.0044530877
## concep_fall 0.005490559 0.01642183233 0.001845775 0.0110338032
## concep_2010 0.011068124 0.00844610317 -0.005886105 -0.0001629937
## concep_2011 -0.022063544 0.01869831001 0.025541096 0.0096091635
## concep_2012 0.002443596 -0.00706763788 -0.004770794 -0.0035360925
## concep_2013 0.007481786 -0.02068066481 -0.014234422 -0.0057396182
## maternal_age 0.030778940 -0.17980907079 -0.095594562 -0.1376124653
## any_smoker -0.008227433 0.02279799333 0.015696371 0.0179541925
## smokeSH -0.011104226 0.04668855425 0.027384613 0.0309364548
## mean_cpss -0.025836085 -0.01114736129 0.017046231 -0.0561153540
## mean_epsd -0.034737548 0.05084465609 0.048585549 0.0670107276
## male 0.029004763 -0.02552947737 -0.033951919 -0.0135085702
## gest_age_w 0.011119160 -0.03926647196 -0.024532454 -0.0076928484
## ed_hs ed_aa ed_4yr low_bmi
## lat -0.01306527915 -0.007178943 0.0022352364 -0.00297745845
## lon 0.04117136599 0.046761047 -0.0076687856 -0.00003551643
## lat_lon_int 0.02686940852 0.024182422 -0.0048607788 0.00245311454
## ed_no_hs -0.02829620561 -0.035455487 -0.0334099777 -0.00399770067
## ed_hs 0.15098194378 -0.042960663 -0.0404821628 -0.00173196369
## ed_aa -0.04296066253 0.178312629 -0.0507246377 0.00786102484
## ed_4yr -0.04048216276 -0.050724638 0.1709517837 -0.00173569637
## low_bmi -0.00173196369 0.007861025 -0.0017356964 0.03236233875
## ovwt_bmi -0.00612657270 0.015075052 0.0040748427 -0.00877179885
## obese_bmi 0.02441297380 0.009478520 -0.0124024526 -0.00668149785
## concep_spring 0.00395788541 0.006761128 -0.0066354615 -0.00501298973
## concep_summer -0.00331835284 -0.011257764 0.0064762004 0.00309812470
## concep_fall 0.00226573698 -0.007084627 0.0010078237 0.00320637243
## concep_2010 0.00576574693 0.004884834 0.0003533604 0.00128404204
## concep_2011 -0.00463350056 0.002410067 0.0053402214 0.00439336479
## concep_2012 0.00371526119 -0.005564182 -0.0061016882 -0.00535266364
## concep_2013 -0.00464096592 -0.002587992 0.0006519748 -0.00028741639
## maternal_age -0.10868310364 -0.040296710 0.1091044519 -0.01089529356
## any_smoker 0.00174689441 0.011063665 -0.0156735248 0.00155279503
## smokeSH 0.02483352246 0.022806677 -0.0362443263 0.00142215122
## mean_cpss -0.03433895561 0.030714793 0.0282429323 0.00484169668
## mean_epsd 0.02014619096 0.025424770 -0.0463684315 0.00946748435
## male 0.00006345557 0.000630823 0.0063679527 -0.00262407430
## gest_age_w -0.01723767893 -0.035168407 0.0301476493 -0.00601412877
## ovwt_bmi obese_bmi concep_spring concep_summer
## lat 0.0205880066 0.0165669344 0.0143292896 -0.01403190526
## lon 0.0051246005 0.0097671301 -0.0004607517 -0.00711327850
## lat_lon_int -0.0150602639 -0.0098964732 -0.0120393632 0.00884440451
## ed_no_hs 0.0045849757 0.0063181836 -0.0002364031 -0.00445308767
## ed_hs -0.0061265727 0.0244129738 0.0039578854 -0.00331835284
## ed_aa 0.0150750518 0.0094785197 0.0067611284 -0.01125776398
## ed_4yr 0.0040748427 -0.0124024526 -0.0066354615 0.00647620043
## low_bmi -0.0087717989 -0.0066814978 -0.0050129897 0.00309812470
## ovwt_bmi 0.1935643614 -0.0523383998 0.0092806876 -0.00512123746
## obese_bmi -0.0523383998 0.1599105152 -0.0085938744 -0.00346392738
## concep_spring 0.0092806876 -0.0085938744 0.1875696767 -0.06020066890
## concep_summer -0.0051212375 -0.0034639274 -0.0602006689 0.18302078356
## concep_fall 0.0026091436 0.0005673674 -0.0677257525 -0.06530697563
## concep_2010 -0.0033345278 -0.0043921206 -0.0236714146 0.00009331701
## concep_2011 0.0055828456 0.0032598742 0.0003633142 -0.00140348782
## concep_2012 -0.0043547938 0.0072737498 -0.0085677457 0.00186260750
## concep_2013 0.0023988692 -0.0059187868 0.0321545529 -0.00028368371
## maternal_age 0.0089002276 0.0027900741 -0.0149065532 0.01490413862
## any_smoker -0.0060656056 0.0027173913 0.0016983696 0.00024262422
## smokeSH -0.0106232083 0.0110524666 -0.0041134138 -0.00627836837
## mean_cpss -0.0082476896 -0.0087226114 0.0079650833 0.01166899615
## mean_epsd -0.0019127169 0.0281330380 -0.0063209443 -0.01563660013
## male 0.0008361204 -0.0017804885 -0.0062746357 -0.00393797778
## gest_age_w -0.0148466585 -0.0214614301 -0.0179961830 0.01920131892
## concep_fall concep_2010 concep_2011 concep_2012
## lat 0.0054905592 0.01106812411 -0.0220635440 0.002443596
## lon 0.0164218323 0.00844610317 0.0186983100 -0.007067638
## lat_lon_int 0.0018457750 -0.00588610547 0.0255410960 -0.004770794
## ed_no_hs 0.0110338032 -0.00016299371 0.0096091635 -0.003536093
## ed_hs 0.0022657370 0.00576574693 -0.0046335006 0.003715261
## ed_aa -0.0070846273 0.00488483437 0.0024100673 -0.005564182
## ed_4yr 0.0010078237 0.00035336041 0.0053402214 -0.006101688
## low_bmi 0.0032063724 0.00128404204 0.0043933648 -0.005352664
## ovwt_bmi 0.0026091436 -0.00333452779 0.0055828456 -0.004354794
## obese_bmi 0.0005673674 -0.00439212056 0.0032598742 0.007273750
## concep_spring -0.0677257525 -0.02367141464 0.0003633142 -0.008567746
## concep_summer -0.0653069756 0.00009331701 -0.0014034878 0.001862608
## concep_fall 0.1977350096 0.02870431199 -0.0127396381 0.001955925
## concep_2010 0.0287043120 0.13567048893 -0.0488918916 -0.047448589
## concep_2011 -0.0127396381 -0.04889189162 0.2110780976 -0.088679776
## concep_2012 0.0019559245 -0.04744858855 -0.0886797758 0.207464863
## concep_2013 -0.0176182513 -0.03914959588 -0.0731692447 -0.071009267
## maternal_age -0.0196470231 -0.02663971411 -0.0380704459 0.031448396
## any_smoker -0.0023777174 0.00266886646 0.0105298913 -0.011015140
## smokeSH -0.0028778966 0.00631569517 0.0136280160 -0.018670867
## mean_cpss -0.0055888831 0.00832724099 -0.0113573536 -0.011161856
## mean_epsd 0.0265650931 -0.01748485806 0.0347867417 -0.022850868
## male 0.0018476768 0.00089584329 -0.0029824116 -0.001761825
## gest_age_w 0.0141959621 0.01072301448 -0.0118973482 -0.026416733
## concep_2013 maternal_age any_smoker smokeSH
## lat 0.0074817863 0.030778940 -0.0082274331 -0.011104226
## lon -0.0206806648 -0.179809071 0.0227979933 0.046688554
## lat_lon_int -0.0142344221 -0.095594562 0.0156963705 0.027384613
## ed_no_hs -0.0057396182 -0.137612465 0.0179541925 0.030936455
## ed_hs -0.0046409659 -0.108683104 0.0017468944 0.024833522
## ed_aa -0.0025879917 -0.040296710 0.0110636646 0.022806677
## ed_4yr 0.0006519748 0.109104452 -0.0156735248 -0.036244326
## low_bmi -0.0002874164 -0.010895294 0.0015527950 0.001422151
## ovwt_bmi 0.0023988692 0.008900228 -0.0060656056 -0.010623208
## obese_bmi -0.0059187868 0.002790074 0.0027173913 0.011052467
## concep_spring 0.0321545529 -0.014906553 0.0016983696 -0.004113414
## concep_summer -0.0002836837 0.014904139 0.0002426242 -0.006278368
## concep_fall -0.0176182513 -0.019647023 -0.0023777174 -0.002877897
## concep_2010 -0.0391495959 -0.026639714 0.0026688665 0.006315695
## concep_2011 -0.0731692447 -0.038070446 0.0105298913 0.013628016
## concep_2012 -0.0710092670 0.031448396 -0.0110151398 -0.018670867
## concep_2013 0.1835981048 0.034822201 -0.0020865683 -0.002101499
## maternal_age 0.0348222009 1.000000000 -0.0466296108 -0.155964054
## any_smoker -0.0020865683 -0.046629611 0.0794836957 0.049010093
## smokeSH -0.0021014990 -0.155964054 0.0490100932 0.191419314
## mean_cpss 0.0104924310 0.100637638 0.0176429080 0.031721118
## mean_epsd 0.0069811381 -0.160410684 0.0421446647 0.108180210
## male 0.0044194935 0.023413804 0.0023291925 0.002004449
## gest_age_w 0.0268056111 0.091663607 -0.0149814181 -0.050311537
## mean_cpss mean_epsd male gest_age_w
## lat -0.025836085 -0.034737548 0.02900476291 0.011119160
## lon -0.011147361 0.050844656 -0.02552947737 -0.039266472
## lat_lon_int 0.017046231 0.048585549 -0.03395191918 -0.024532454
## ed_no_hs -0.056115354 0.067010728 -0.01350857023 -0.007692848
## ed_hs -0.034338956 0.020146191 0.00006345557 -0.017237679
## ed_aa 0.030714793 0.025424770 0.00063082298 -0.035168407
## ed_4yr 0.028242932 -0.046368432 0.00636795270 0.030147649
## low_bmi 0.004841697 0.009467484 -0.00262407430 -0.006014129
## ovwt_bmi -0.008247690 -0.001912717 0.00083612040 -0.014846658
## obese_bmi -0.008722611 0.028133038 -0.00178048853 -0.021461430
## concep_spring 0.007965083 -0.006320944 -0.00627463569 -0.017996183
## concep_summer 0.011668996 -0.015636600 -0.00393797778 0.019201319
## concep_fall -0.005588883 0.026565093 0.00184767678 0.014195962
## concep_2010 0.008327241 -0.017484858 0.00089584329 0.010723014
## concep_2011 -0.011357354 0.034786742 -0.00298241161 -0.011897348
## concep_2012 -0.011161856 -0.022850868 -0.00176182513 -0.026416733
## concep_2013 0.010492431 0.006981138 0.00441949355 0.026805611
## maternal_age 0.100637638 -0.160410684 0.02341380415 0.091663607
## any_smoker 0.017642908 0.042144665 0.00232919255 -0.014981418
## smokeSH 0.031721118 0.108180210 0.00200444935 -0.050311537
## mean_cpss 1.000000000 0.455187203 -0.00331530432 -0.037142336
## mean_epsd 0.455187203 1.000000000 0.00154181454 -0.137187808
## male -0.003315304 0.001541815 0.25014184185 -0.007427180
## gest_age_w -0.037142336 -0.137187808 -0.00742717951 1.000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Response data: birth weight (in grams)
Y <- select(hs_data2, birth_weight) %>%
as.matrix()
head(Y)## birth_weight
## [1,] 2860
## [2,] 2755
## [3,] 3505
## [4,] 2695
## [5,] 3355
## [6,] 3810Distribution of birth weight and scaled birth weight
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
Dropping gest_age_w from the covariates
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"2 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 891.2509#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(bw_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 21 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(bw_ridge)## 22 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 3756.2244127611
## mean_pm 6.5831658736
## mean_o3 -5.7909309972
## mean_temp -2.6190406717
## pct_tree_cover 0.0346391254
## pct_impervious -0.4281346032
## mean_aadt_intensity -0.0002915500
## dist_m_tri -0.0003520682
## dist_m_npl 0.0001168135
## dist_m_waste_site 0.0017447014
## dist_m_major_emit -0.0003705192
## dist_m_cafo -0.0003121004
## dist_m_mine_well -0.0022906005
## cvd_rate_adj -0.1469368176
## res_rate_adj -0.1446242346
## violent_crime_rate -0.4156388202
## property_crime_rate -0.0143345439
## pct_less_hs -0.6736508410
## pct_unemp -3.6551596165
## pct_limited_eng -0.5218862220
## pct_hh_pov -0.4758794734
## pct_poc -0.4466466437Ridge regression predictions
ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.
3 Nonparametric Bayesian Shrinkage (NPB): Birth weight
3.1 Finding the NPB priors
3.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.05907077 1.7292064 0.000000 0 0.008
## [2,] -1.18173936 6.7453018 -22.846654 0 0.050
## [3,] -0.68874315 5.1022188 -3.829552 0 0.032
## [4,] -0.09836726 1.3523591 0.000000 0 0.014
## [5,] -0.58334088 4.2590450 -2.025017 0 0.028
## [6,] -0.02810779 1.3627030 0.000000 0 0.018
## [7,] -0.07241864 1.6862869 0.000000 0 0.010
## [8,] 0.12843949 1.6692407 0.000000 0 0.016
## [9,] 0.29614136 3.3791200 0.000000 0 0.020
## [10,] -0.04574610 1.1661326 0.000000 0 0.010
## [11,] -1.02549044 12.1015196 -21.361864 0 0.048
## [12,] -0.76889738 5.1972449 -7.703709 0 0.032
## [13,] -0.50082159 4.2854699 -1.645144 0 0.028
## [14,] -0.52647452 4.1378266 0.000000 0 0.020
## [15,] -0.14443889 1.7466026 0.000000 0 0.018
## [16,] -0.03206135 0.8482502 0.000000 0 0.012
## [17,] -0.71146302 4.8104069 -9.104986 0 0.032
## [18,] -6.57484938 17.6038554 -65.994065 0 0.150
## [19,] -0.32089031 3.4509916 0.000000 0 0.016
## [20,] -0.21027072 2.1926996 0.000000 0 0.016
## [21,] -0.63622272 5.4262819 0.000000 0 0.026plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.37835158 6.444211 -12.39843 15.459027 0.254
## [2,] -6.50866456 13.285146 -47.61147 5.157978 0.422
## [3,] -2.99829637 9.530987 -27.10395 9.170820 0.316
## [4,] -1.83469729 7.302263 -20.66994 8.664141 0.302
## [5,] -4.15010395 8.878299 -31.18568 1.432763 0.364
## [6,] -1.13456265 5.999765 -13.20965 9.648707 0.262
## [7,] -1.06393850 6.067273 -14.88747 10.146850 0.274
## [8,] -0.41269500 6.179682 -13.50993 11.850908 0.238
## [9,] 0.08388743 7.009746 -12.23644 21.113180 0.262
## [10,] -0.45998103 6.272873 -11.69475 11.850908 0.238
## [11,] -2.86724980 11.352373 -33.00612 8.125983 0.348
## [12,] -3.68104712 8.584663 -26.86129 3.369650 0.354
## [13,] -3.81491402 8.769486 -30.58368 3.211650 0.382
## [14,] -3.48433858 7.905814 -25.16353 3.591160 0.354
## [15,] -1.13941047 5.331153 -14.58868 4.475193 0.232
## [16,] -2.06055760 6.610397 -19.45050 7.383645 0.310
## [17,] -2.67440654 7.648666 -25.96178 7.642657 0.336
## [18,] -17.54869944 23.031327 -74.98278 0.000000 0.664
## [19,] -2.39876713 6.867868 -19.15311 7.383645 0.338
## [20,] -2.19811559 7.659921 -22.28194 8.860543 0.332
## [21,] -2.38098284 7.546698 -22.00851 9.174345 0.372plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
3.2 Fit the NPB model without temperature
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures (minus temperature)
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v4a.1.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.1.rdata"))
npb.sum <- summary(fit.npb)3.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -0.64125098 5.911603 -15.455836 10.490517 0.1816
## mean_o3 -126.48202072 96.518824 -285.016660 3.445415 0.8044
## pct_tree_cover -0.68083059 5.615548 -15.848685 10.739415 0.1900
## pct_impervious -2.83488760 8.796487 -29.792364 5.146130 0.2520
## mean_aadt_intensity -0.18793856 4.988127 -11.993448 10.921741 0.1692
## dist_m_tri -0.76891442 6.081892 -17.209786 10.305810 0.1928
## dist_m_npl 0.34958475 5.844586 -10.729199 14.822900 0.1804
## dist_m_waste_site 1.45511736 8.095672 -9.515091 26.912081 0.1968
## dist_m_major_emit -0.08282941 5.378265 -12.159189 12.434891 0.1872
## dist_m_cafo -4.47615039 22.150639 -62.347984 14.992358 0.2892
## dist_m_mine_well -2.67188258 9.303658 -32.030285 6.776363 0.2448
## cvd_rate_adj -2.62833089 8.514285 -29.765889 4.970325 0.2524
## res_rate_adj -3.01604247 9.570154 -32.440411 6.576391 0.2644
## violent_crime_rate -0.14945003 5.737088 -12.685065 11.958291 0.1824
## property_crime_rate -0.77234125 5.314391 -15.612152 8.053212 0.1860
## pct_less_hs -1.42774630 7.154552 -22.018857 8.044627 0.2156
## pct_unemp -23.79952093 28.421158 -87.511759 0.000000 0.6100
## pct_limited_eng -1.34682390 6.381113 -18.977246 7.841900 0.2012
## pct_hh_pov -1.24705339 7.810668 -22.139205 10.796265 0.2196
## pct_poc -1.54490752 8.140743 -22.840185 10.342720 0.23083.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum$covariates)[2:nrow(npb.sum$covariates)] <- colnames(W.scaled2)
npb.sum$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3142.948138 221.23796 2710.59014 3591.61617
## lat -8.852688 321.03802 -629.26824 598.31505
## lon 9.480748 153.06032 -279.27296 313.46058
## lat_lon_int 5.253298 387.46373 -747.98136 749.95032
## ed_no_hs 115.687118 76.71295 -32.87543 264.35342
## ed_hs 79.896671 69.27289 -57.10504 217.14594
## ed_aa 23.670895 60.11343 -94.17007 141.15205
## ed_4yr 67.124514 51.23803 -33.42328 169.58831
## low_bmi -72.184590 94.60050 -258.25729 119.68684
## ovwt_bmi 36.667903 41.33308 -41.92536 116.63096
## obese_bmi 112.604235 47.48015 18.38811 203.90394
## concep_spring -84.665927 101.94369 -239.82139 142.88394
## concep_summer -76.640630 131.37631 -336.69138 131.19268
## concep_fall -2.615382 89.46707 -183.37690 149.74649
## concep_2010 26.233351 217.00773 -417.31469 442.84115
## concep_2011 20.545505 215.93813 -408.59408 438.95755
## concep_2012 32.381563 216.32135 -402.50133 453.21728
## concep_2013 109.276001 217.54812 -315.18924 534.05497
## maternal_age 76.623361 22.76444 31.48236 121.65840
## any_smoker -140.725626 64.24669 -265.38100 -11.72093
## smokeSH -113.196362 44.47163 -200.08707 -26.22239
## mean_cpss 11.860854 20.41184 -26.66242 54.29258
## mean_epsd -51.380871 20.56738 -92.05272 -11.43408
## male 166.313157 34.15550 98.80753 230.260033.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.017438215244 0.908986942 0.0000 0.0000 0.0012
## [2,] -0.001570933914 0.321889805 0.0000 0.0000 0.0012
## [3,] -0.005050155089 0.269284590 0.0000 0.0000 0.0008
## [4,] -0.000899881214 0.044994061 0.0000 0.0000 0.0004
## [5,] 0.001401134043 0.070056702 0.0000 0.0000 0.0004
## [6,] 0.006066131113 0.487992896 0.0000 0.0000 0.0020
## [7,] -0.002022843832 0.207040988 0.0000 0.0000 0.0008
## [8,] -0.003443891433 0.172194572 0.0000 0.0000 0.0004
## [9,] -0.012746513228 0.380095974 0.0000 0.0000 0.0016
## [10,] -0.012954477025 0.447726805 0.0000 0.0000 0.0012
## [11,] -0.007529079003 0.499802518 0.0000 0.0000 0.0020
## [12,] 0.004234366871 0.174822849 0.0000 0.0000 0.0008
## [13,] -0.000522542019 0.018663667 0.0000 0.0000 0.0008
## [14,] 0.002684209813 0.491394168 0.0000 0.0000 0.0016
## [15,] -0.002685413318 0.102346907 0.0000 0.0000 0.0008
## [16,] 0.003675129802 0.135131564 0.0000 0.0000 0.0008
## [17,] -0.021002092163 0.971540034 0.0000 0.0000 0.0012
## [18,] 0.010293649736 0.436031850 0.0000 0.0000 0.0008
## [19,] -0.003677054422 0.141189576 0.0000 0.0000 0.0008
## [20,] -0.013623634880 0.482453807 0.0000 0.0000 0.0020
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## [577,] -0.059857362648 2.821409134 0.0000 0.0000 0.0024
## [578,] -0.082423741515 2.711199122 0.0000 0.0000 0.0024
## [579,] -0.001539630212 0.135373632 0.0000 0.0000 0.0008
## [580,] -0.001881249357 0.102091001 0.0000 0.0000 0.0008
## [581,] -0.273424567937 4.702648379 0.0000 0.0000 0.0044
## [582,] -0.014882700089 1.074945145 0.0000 0.0000 0.0020
## [583,] -0.051432024167 1.498641348 0.0000 0.0000 0.0024
## [584,] -0.030154159928 1.313038874 0.0000 0.0000 0.0020
## [585,] -0.015113578472 0.927404907 0.0000 0.0000 0.0028
## [586,] 0.013488312390 0.529563578 0.0000 0.0000 0.0012
## [587,] -0.066288396181 1.942594865 0.0000 0.0000 0.0028
## [588,] 0.005366907139 0.509481097 0.0000 0.0000 0.0024
## [589,] -0.075516110774 3.081729763 0.0000 0.0000 0.0020
## [590,] -0.006622353921 0.305550680 0.0000 0.0000 0.0012
## [591,] 0.030377516261 1.381042758 0.0000 0.0000 0.0012
## [592,] -0.027925282276 1.703327605 0.0000 0.0000 0.0016
## [593,] -0.006673696594 0.796966429 0.0000 0.0000 0.0016
## [594,] -0.003944013945 0.404333389 0.0000 0.0000 0.0008
## [595,] 0.041033325033 1.410800229 0.0000 0.0000 0.0028
## [596,] -0.088249846552 2.585429286 0.0000 0.0000 0.0028
## [597,] 0.076040591351 2.087619634 0.0000 0.0000 0.0016
## [598,] -0.005347921639 0.299900920 0.0000 0.0000 0.0016
## [599,] -0.003443891433 0.172194572 0.0000 0.0000 0.0004
## [600,] -0.089966071692 2.943008324 0.0000 0.0000 0.0024
## [601,] -0.007537898449 0.509725000 0.0000 0.0000 0.0020
## [602,] 0.000355426098 0.102414359 0.0000 0.0000 0.0008
## [603,] 0.023383775505 0.768320558 0.0000 0.0000 0.0016
## [604,] -0.010267419005 0.582536774 0.0000 0.0000 0.0008
## [605,] 0.012836131413 0.476034309 0.0000 0.0000 0.0012
## [606,] -0.027646032585 0.885966621 0.0000 0.0000 0.0016
## [607,] -0.022748118392 1.029150878 0.0000 0.0000 0.0012
## [608,] -0.021068459704 1.133299454 0.0000 0.0000 0.0016
## [609,] -0.006110262875 0.191139753 0.0000 0.0000 0.0012
## [610,] -0.014722035733 1.005118281 0.0000 0.0000 0.0036
## [611,] 0.025729418296 0.814658457 0.0000 0.0000 0.0012
## [612,] 0.015125634248 0.955354419 0.0000 0.0000 0.0028
## [613,] -0.005630800949 0.380966473 0.0000 0.0000 0.0012
## [614,] 0.005567069839 0.813550005 0.0000 0.0000 0.0020
## [615,] -0.005487556507 0.200195669 0.0000 0.0000 0.0008
## [616,] -0.000506252733 0.025312637 0.0000 0.0000 0.0004
## [617,] -0.003764185227 0.371384972 0.0000 0.0000 0.0028
## [618,] 0.012134801995 0.606740100 0.0000 0.0000 0.0004
## [619,] -0.001384675744 0.178573365 0.0000 0.0000 0.0008
## [620,] 0.202873356065 4.580754569 0.0000 0.0000 0.0036
## [621,] -0.001983314158 0.099165708 0.0000 0.0000 0.0004
## [622,] 0.007013546677 0.255566204 0.0000 0.0000 0.0008
## [623,] -0.036270976639 1.822863150 0.0000 0.0000 0.0024
## [624,] 0.000848293967 0.183837266 0.0000 0.0000 0.0016
## [625,] -0.011977627499 0.425577713 0.0000 0.0000 0.0008
## [626,] -0.003217057662 0.332184789 0.0000 0.0000 0.0024
## [627,] 0.001749630365 0.087481518 0.0000 0.0000 0.0004
## [628,] -0.026009904267 0.796874583 0.0000 0.0000 0.0028
## [629,] -0.046105393163 1.461744462 0.0000 0.0000 0.0016
## [630,] -0.006275205220 0.604332575 0.0000 0.0000 0.0020
## [631,] -0.002603875800 0.302679952 0.0000 0.0000 0.0016
## [632,] 0.052034449028 2.375218521 0.0000 0.0000 0.0012
## [633,] -0.026511033843 1.144500222 0.0000 0.0000 0.0012
## [634,] -0.005099673018 0.254983651 0.0000 0.0000 0.0004
## [635,] -0.014182404061 0.886621189 0.0000 0.0000 0.0020
## [636,] 0.003110978758 0.155548938 0.0000 0.0000 0.0004
## [637,] -0.034119827898 1.089285569 0.0000 0.0000 0.0024
## [638,] -0.027586287285 1.709753842 0.0000 0.0000 0.0012
## [639,] 0.009966849736 0.410118400 0.0000 0.0000 0.0016
## [640,] -0.105488693433 2.663842527 0.0000 0.0000 0.0032
## [641,] -0.005135510457 0.354029314 0.0000 0.0000 0.0012
## [642,] -0.640510290189 8.719694453 0.0000 0.0000 0.0080
## [643,] 0.361484644902 6.896079382 0.0000 0.0000 0.0036
## [644,] -0.003489137480 0.447002294 0.0000 0.0000 0.0020
## [645,] -0.005109810825 0.255490541 0.0000 0.0000 0.0004
## [646,] -0.002286929002 0.709971694 0.0000 0.0000 0.0028
## [647,] -0.010898382309 0.385607247 0.0000 0.0000 0.0020
## [648,] -0.013898107209 0.674005366 0.0000 0.0000 0.0028
## [649,] -0.009880247074 0.342066072 0.0000 0.0000 0.0012
## [650,] 0.010660517262 0.459402439 0.0000 0.0000 0.00083.2.4 Predict fitted values for each individual
pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals3.2.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")
3.3 Run the NPB model with temperaure and ozone
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4a.2.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.2.rdata"))
npb.sum2 <- summary(fit.npb2)3.3.1 First, main effect regression coefficients with PIPs
rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -6.4455763 14.489731 -51.36621 2.683216 0.3900
## mean_o3 -11.0042874 22.752166 -77.86027 2.341424 0.4668
## mean_temp -1.0527040 21.370684 -31.95659 15.886379 0.3216
## pct_tree_cover -2.0605910 6.449766 -19.12039 5.108510 0.2828
## pct_impervious -2.9374980 7.398262 -25.44654 1.796266 0.3024
## mean_aadt_intensity -0.8049048 5.433489 -14.31492 8.551697 0.2352
## dist_m_tri -2.1739110 6.890125 -21.93467 6.114000 0.2940
## dist_m_npl -0.9900659 5.268705 -14.29863 6.505562 0.2416
## dist_m_waste_site 0.4862897 7.223983 -11.84406 21.160154 0.2316
## dist_m_major_emit -0.8789868 5.184028 -14.26873 8.054941 0.2276
## dist_m_cafo -4.6180766 17.227018 -44.13164 9.197160 0.3720
## dist_m_mine_well -2.9322838 8.180628 -26.42892 5.800016 0.3208
## cvd_rate_adj -3.0336843 7.593749 -26.24958 4.104509 0.3336
## res_rate_adj -3.6478780 8.345746 -28.46638 2.910625 0.3524
## violent_crime_rate -1.0976867 5.955153 -15.26852 6.775785 0.2476
## property_crime_rate -2.1636489 6.153787 -19.26523 4.354570 0.2876
## pct_less_hs -3.1518381 8.226334 -26.93850 4.009727 0.3264
## pct_unemp -15.7384162 21.089822 -73.05732 0.000000 0.6156
## pct_limited_eng -2.5649220 7.175619 -23.53298 2.606821 0.2868
## pct_hh_pov -2.5735162 7.067605 -22.47381 2.354691 0.2944
## pct_poc -2.6849906 8.157365 -25.36287 4.181035 0.30363.3.2 Next, posterior means and CIs for covariates
rownames(npb.sum2$covariates)[2:nrow(npb.sum2$covariates)] <- colnames(W.scaled2)
npb.sum2$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3158.7866392 218.49084 2738.15525 3591.270162
## lat -5.0778647 318.75678 -649.07654 598.794237
## lon -1.3163246 150.21131 -287.16996 301.070988
## lat_lon_int 0.9070337 383.25676 -771.57336 722.890601
## ed_no_hs 103.1285462 74.18587 -39.66910 245.517908
## ed_hs 76.2040362 66.87147 -55.56263 204.601927
## ed_aa 20.0923263 59.17875 -93.04662 135.665131
## ed_4yr 70.6485305 51.99147 -31.84932 170.862585
## low_bmi -70.4808587 92.21677 -253.62142 108.880019
## ovwt_bmi 43.3279289 39.76495 -36.11728 123.375098
## obese_bmi 119.2426138 44.62636 31.44680 205.620085
## concep_spring -82.6547585 55.25862 -186.16906 35.606865
## concep_summer -50.0030742 79.87508 -213.49674 91.265229
## concep_fall 70.9309202 66.48993 -56.25536 209.449908
## concep_2010 -1.2050533 217.99544 -433.49723 417.598929
## concep_2011 12.5723009 217.17112 -411.09172 433.388265
## concep_2012 70.6052139 217.48723 -351.09090 492.224084
## concep_2013 129.9476757 214.70349 -287.84362 529.665067
## maternal_age 69.4292496 21.80828 25.79014 110.086956
## any_smoker -162.9538912 62.46679 -289.55835 -42.591510
## smokeSH -82.2831407 43.82815 -171.61774 1.782190
## mean_cpss 3.1369961 19.19174 -33.38475 41.404436
## mean_epsd -43.9248511 19.84420 -81.46977 -4.993641
## male 171.9552244 31.88727 106.91092 234.4151503.3.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum2$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 1.194658926659 8.57711879 0.00000 0.0000 0.0216
## [2,] 1.052533086230 8.03807503 0.00000 0.0000 0.0200
## [3,] -0.003185446482 0.92512170 0.00000 0.0000 0.0024
## [4,] -0.018234201891 0.52129268 0.00000 0.0000 0.0016
## [5,] 0.014956771419 0.49698695 0.00000 0.0000 0.0012
## [6,] -0.004561501319 0.36148257 0.00000 0.0000 0.0028
## [7,] -0.018155212716 0.59266879 0.00000 0.0000 0.0020
## [8,] -0.012546584738 0.44681547 0.00000 0.0000 0.0016
## [9,] -0.016837852880 0.45595145 0.00000 0.0000 0.0036
## [10,] -0.042703830606 0.82466283 0.00000 0.0000 0.0036
## [11,] 0.001608820602 0.34180533 0.00000 0.0000 0.0028
## [12,] -0.021844129742 0.56526999 0.00000 0.0000 0.0028
## [13,] -0.009765518433 0.39451776 0.00000 0.0000 0.0032
## [14,] -0.035696541157 0.77000573 0.00000 0.0000 0.0032
## [15,] -0.002621529365 0.27549081 0.00000 0.0000 0.0008
## [16,] -0.033604211639 0.78382068 0.00000 0.0000 0.0040
## [17,] -0.013301097351 0.42436228 0.00000 0.0000 0.0016
## [18,] -0.090105690587 1.69999876 0.00000 0.0000 0.0056
## [19,] -0.005049895956 0.19066975 0.00000 0.0000 0.0008
## [20,] -0.014803432043 0.67378729 0.00000 0.0000 0.0032
## [21,] -171.586953546664 32.64089047 -241.01292 -120.2583 1.0000
## [22,] -0.013635922495 0.35496660 0.00000 0.0000 0.0020
## [23,] -0.012682016081 0.39454924 0.00000 0.0000 0.0016
## [24,] -0.003734548575 0.42229682 0.00000 0.0000 0.0012
## [25,] -0.029055286362 0.67199799 0.00000 0.0000 0.0028
## [26,] -0.018132591417 0.52436740 0.00000 0.0000 0.0016
## [27,] -0.113254844358 1.90957615 0.00000 0.0000 0.0052
## [28,] -0.006644755107 0.46889824 0.00000 0.0000 0.0016
## [29,] -0.009598516058 0.34205166 0.00000 0.0000 0.0008
## [30,] -0.034347717584 0.85181540 0.00000 0.0000 0.0028
## [31,] 0.011819037075 0.56315276 0.00000 0.0000 0.0020
## [32,] -0.003461516042 0.20446331 0.00000 0.0000 0.0008
## [33,] -0.005769212102 0.18179199 0.00000 0.0000 0.0012
## [34,] 0.000000000000 0.00000000 0.00000 0.0000 0.0000
## [35,] 0.034329455299 1.02874325 0.00000 0.0000 0.0032
## [36,] 0.032492362349 1.03409558 0.00000 0.0000 0.0016
## [37,] 0.000891031862 0.08448097 0.00000 0.0000 0.0012
## [38,] 0.090980960008 2.21371528 0.00000 0.0000 0.0028
## [39,] -0.010382011432 0.36864675 0.00000 0.0000 0.0020
## [40,] -0.016138476375 0.41620817 0.00000 0.0000 0.0024
## [41,] -0.009839010850 0.48059257 0.00000 0.0000 0.0012
## [42,] 0.008104598286 0.22550419 0.00000 0.0000 0.0016
## [43,] -0.013429211899 0.57948800 0.00000 0.0000 0.0048
## [44,] -0.003394295259 0.28235672 0.00000 0.0000 0.0012
## [45,] -0.042573667130 0.95713794 0.00000 0.0000 0.0044
## [46,] -0.000826406587 0.40118896 0.00000 0.0000 0.0020
## [47,] -0.026966543148 0.75806092 0.00000 0.0000 0.0032
## [48,] -0.007680688178 0.21704419 0.00000 0.0000 0.0016
## [49,] 0.008117026562 0.87097121 0.00000 0.0000 0.0020
## [50,] 0.006346531419 0.38928508 0.00000 0.0000 0.0016
## [51,] -0.021299448942 0.55958888 0.00000 0.0000 0.0024
## [52,] 0.013693274673 1.02422534 0.00000 0.0000 0.0016
## [53,] 0.024996903348 1.08308278 0.00000 0.0000 0.0024
## [54,] 0.018574679160 0.94261883 0.00000 0.0000 0.0016
## [55,] -0.024362560567 0.57485796 0.00000 0.0000 0.0028
## [56,] 0.001678042324 0.37343646 0.00000 0.0000 0.0016
## [57,] -0.003953868511 0.16685696 0.00000 0.0000 0.0012
## [58,] -0.004799610070 0.25122579 0.00000 0.0000 0.0008
## [59,] -0.013293622476 0.55843588 0.00000 0.0000 0.0020
## [60,] -0.008947024374 0.54136289 0.00000 0.0000 0.0024
## [61,] -0.031357955854 1.06565322 0.00000 0.0000 0.0028
## [62,] 0.015880659888 0.66992662 0.00000 0.0000 0.0024
## [63,] 0.040153744116 1.67909645 0.00000 0.0000 0.0028
## [64,] -0.020421245428 0.54028258 0.00000 0.0000 0.0028
## [65,] -0.016600414772 0.40215708 0.00000 0.0000 0.0028
## [66,] 0.000832641679 0.03198112 0.00000 0.0000 0.0012
## [67,] 0.000313880310 0.13587445 0.00000 0.0000 0.0016
## [68,] -0.012904860091 0.33997237 0.00000 0.0000 0.0016
## [69,] -0.012906985427 0.37150742 0.00000 0.0000 0.0024
## [70,] -0.014995334410 0.45596885 0.00000 0.0000 0.0020
## [71,] -0.008608882464 0.46065656 0.00000 0.0000 0.0008
## [72,] 0.003825531837 0.41208515 0.00000 0.0000 0.0008
## [73,] 0.025834609207 0.76024914 0.00000 0.0000 0.0016
## [74,] -0.004848640804 0.19505860 0.00000 0.0000 0.0008
## [75,] -0.000423103699 0.66000525 0.00000 0.0000 0.0016
## [76,] 0.007639130633 0.41240669 0.00000 0.0000 0.0028
## [77,] 0.003876165318 0.59269436 0.00000 0.0000 0.0012
## [78,] -0.001811329169 0.31879677 0.00000 0.0000 0.0020
## [79,] -0.003734793780 0.18673969 0.00000 0.0000 0.0004
## [80,] -0.027933645383 0.68769370 0.00000 0.0000 0.0024
## [81,] 0.002650860284 0.57650950 0.00000 0.0000 0.0024
## [82,] -0.016887597673 0.43320387 0.00000 0.0000 0.0016
## [83,] -0.019308661504 0.95671561 0.00000 0.0000 0.0020
## [84,] 0.000330648547 0.14159500 0.00000 0.0000 0.0008
## [85,] -0.013388069237 0.51592470 0.00000 0.0000 0.0028
## [86,] -0.014441395277 0.51131969 0.00000 0.0000 0.0024
## [87,] -0.008416476950 0.26162437 0.00000 0.0000 0.0016
## [88,] -0.005732547922 0.20673934 0.00000 0.0000 0.0012
## [89,] -0.000857799082 0.05895210 0.00000 0.0000 0.0008
## [90,] 0.000683600453 0.03418002 0.00000 0.0000 0.0004
## [91,] 0.003851299075 0.38392497 0.00000 0.0000 0.0016
## [92,] -0.007454980732 0.41341438 0.00000 0.0000 0.0016
## [93,] 0.015001946600 0.43997718 0.00000 0.0000 0.0016
## [94,] 0.017991156456 0.70262373 0.00000 0.0000 0.0024
## [95,] -0.015076054331 0.73672139 0.00000 0.0000 0.0020
## [96,] -0.002107585358 0.14812449 0.00000 0.0000 0.0012
## [97,] -0.009268562489 0.38915641 0.00000 0.0000 0.0028
## [98,] -0.018475394186 0.49671920 0.00000 0.0000 0.0016
## [99,] -0.010059720923 0.41898146 0.00000 0.0000 0.0032
## [100,] -0.022049857681 0.66317079 0.00000 0.0000 0.0024
## [101,] -0.000393655823 0.34043129 0.00000 0.0000 0.0016
## [102,] -0.015397807544 0.47746187 0.00000 0.0000 0.0020
## [103,] 0.001272539714 0.23593355 0.00000 0.0000 0.0016
## [104,] -0.009892363892 0.59665144 0.00000 0.0000 0.0020
## [105,] 0.007747953187 0.33554846 0.00000 0.0000 0.0008
## [106,] -0.004709086305 0.17474516 0.00000 0.0000 0.0008
## [107,] -0.000460775722 0.44833311 0.00000 0.0000 0.0024
## [108,] -0.004805551141 0.56405991 0.00000 0.0000 0.0020
## [109,] 0.001923025411 0.28114255 0.00000 0.0000 0.0024
## [110,] -0.006284330981 0.35295907 0.00000 0.0000 0.0016
## [111,] 0.015440379558 1.07384143 0.00000 0.0000 0.0032
## [112,] 0.004602746801 0.56758717 0.00000 0.0000 0.0028
## [113,] -0.017735981111 0.54082001 0.00000 0.0000 0.0012
## [114,] -0.010477644173 0.35254096 0.00000 0.0000 0.0016
## [115,] -0.004642558155 0.13795289 0.00000 0.0000 0.0020
## [116,] 0.033984364493 1.00079740 0.00000 0.0000 0.0016
## [117,] 0.005451446967 0.58457171 0.00000 0.0000 0.0020
## [118,] 0.035349518956 1.06691479 0.00000 0.0000 0.0020
## [119,] -0.003648434595 0.50870251 0.00000 0.0000 0.0020
## [120,] -0.000406517433 0.55694524 0.00000 0.0000 0.0036
## [121,] -0.000963162730 0.04815814 0.00000 0.0000 0.0004
## [122,] -0.010886914652 0.29603307 0.00000 0.0000 0.0020
## [123,] -0.004181084324 0.20905422 0.00000 0.0000 0.0004
## [124,] -0.002813651968 0.15860679 0.00000 0.0000 0.0016
## [125,] 0.002412117795 0.07549225 0.00000 0.0000 0.0012
## [126,] 0.001875640973 0.22705145 0.00000 0.0000 0.0008
## [127,] 0.008956258568 0.42606253 0.00000 0.0000 0.0016
## [128,] -0.005605121654 0.31091848 0.00000 0.0000 0.0008
## [129,] -0.021503640232 0.60632185 0.00000 0.0000 0.0020
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## [684,] 0.004567504779 0.67764079 0.00000 0.0000 0.0020
## [685,] -1.754547128681 15.22012268 0.00000 0.0000 0.0156
## [686,] 1.653403614093 13.90185621 0.00000 0.0000 0.0188
## [687,] -0.068474491864 2.52800112 0.00000 0.0000 0.0028
## [688,] 0.001661340212 0.36765531 0.00000 0.0000 0.0024
## [689,] -0.182967651174 5.65166770 0.00000 0.0000 0.0036
## [690,] -0.008267804300 0.59744544 0.00000 0.0000 0.0032
## [691,] -0.015746654977 0.50950701 0.00000 0.0000 0.0020
## [692,] -0.008984176592 0.28700121 0.00000 0.0000 0.0012
## [693,] -0.012934723969 0.40373791 0.00000 0.0000 0.00163.3.4 Predict fitted values for each individual
pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals3.3.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")
3.4 Fit the NPB model without ozone and with temperature
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone but with temperature just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb3 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb3, file = here::here("Results", "NPB_Birth_Weight_v4a.3.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.3.rdata"))
npb.sum3 <- summary(fit.npb3)3.4.1 First, main effect regression coefficients with PIPs
rownames(npb.sum3$main.effects) <- colnames(X.scaled[,-c(2)])
npb.sum3$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -6.2270028 11.829903 -40.83325 1.3329720 0.4216
## mean_temp -5.9078416 14.521641 -48.41181 3.9188396 0.3936
## pct_tree_cover -1.9400109 6.176479 -18.85633 5.1386887 0.2768
## pct_impervious -3.8993339 8.193060 -28.11322 0.6778887 0.3512
## mean_aadt_intensity -1.2645979 5.587482 -15.30176 6.5179151 0.2332
## dist_m_tri -1.8403906 7.008697 -21.51611 9.4004148 0.2732
## dist_m_npl -0.6330595 6.362851 -15.29715 12.8578425 0.2448
## dist_m_waste_site -0.4297864 6.516643 -14.28281 13.9915356 0.2332
## dist_m_major_emit -0.5368893 6.054691 -13.79800 11.8574575 0.2272
## dist_m_cafo -3.3788146 13.135915 -32.52030 8.8764179 0.3396
## dist_m_mine_well -4.9812807 10.496138 -35.19974 2.8591574 0.3868
## cvd_rate_adj -4.0803243 9.027007 -29.75359 2.0091130 0.3660
## res_rate_adj -4.6358931 9.454517 -31.85015 1.8292630 0.3928
## violent_crime_rate -1.1196381 6.014000 -16.29494 7.4135878 0.2476
## property_crime_rate -2.1919509 6.251015 -18.80068 2.8857337 0.2760
## pct_less_hs -2.9564607 7.425378 -24.09712 4.3310094 0.3324
## pct_unemp -12.3136410 17.898237 -62.01418 0.0000000 0.5756
## pct_limited_eng -2.4849233 7.052612 -21.98537 3.2781220 0.2932
## pct_hh_pov -2.2683344 6.679594 -19.73307 4.6395661 0.2964
## pct_poc -3.0137492 7.665084 -25.22988 3.7484350 0.31803.4.2 Next, posterior means and CIs for covariates
rownames(npb.sum3$covariates)[2:nrow(npb.sum3$covariates)] <- colnames(W.scaled2)
npb.sum3$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3058.442273 219.05707 2620.58039 3498.442014
## lat -5.999754 318.89735 -608.36191 623.377269
## lon 10.546695 152.15860 -288.06563 299.195424
## lat_lon_int 7.195182 385.14524 -728.60902 776.523923
## ed_no_hs 128.616117 74.63545 -18.48899 272.062718
## ed_hs 95.741646 66.78362 -34.93224 225.182912
## ed_aa 39.261940 59.36616 -77.55912 152.325102
## ed_4yr 72.228575 50.91669 -26.20372 174.118664
## low_bmi -65.473942 92.40772 -247.48219 119.485254
## ovwt_bmi 37.317858 39.20717 -39.40143 112.156034
## obese_bmi 100.422704 45.68430 8.69515 187.501340
## concep_spring 341.338572 78.56078 188.12131 496.239239
## concep_summer 59.381409 50.90035 -41.29376 154.152368
## concep_fall 357.791243 78.83716 204.71163 502.817734
## concep_2010 -4.131619 216.93677 -447.85147 415.492330
## concep_2011 -63.978522 216.63831 -492.09241 367.394511
## concep_2012 3.946398 216.53151 -434.74359 427.725231
## concep_2013 55.121301 215.79316 -376.40130 483.566588
## maternal_age 81.511954 21.99303 39.50672 125.837419
## any_smoker -137.171944 60.97173 -255.55101 -15.501723
## smokeSH -111.126885 42.72822 -194.76406 -27.370965
## mean_cpss 11.338319 19.24256 -25.76778 49.134449
## mean_epsd -45.061018 20.08659 -83.95663 -4.903774
## male 167.351395 33.20811 103.51980 230.9233443.4.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum3$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.000376303369 0.25387243 0.0000 0.0000 0.0024
## [2,] -0.006764598353 0.33397270 0.0000 0.0000 0.0024
## [3,] -0.006935068553 0.22970068 0.0000 0.0000 0.0020
## [4,] 0.015805756547 0.60557707 0.0000 0.0000 0.0012
## [5,] -0.006043426468 0.17538887 0.0000 0.0000 0.0012
## [6,] 0.001295340895 0.45616661 0.0000 0.0000 0.0028
## [7,] -0.017682733203 0.43962863 0.0000 0.0000 0.0024
## [8,] -0.007409563610 0.57893001 0.0000 0.0000 0.0060
## [9,] -0.019516770679 0.47299718 0.0000 0.0000 0.0028
## [10,] -0.013874626769 0.33988058 0.0000 0.0000 0.0032
## [11,] -0.011215927711 0.30262510 0.0000 0.0000 0.0028
## [12,] -0.017190382562 0.63066133 0.0000 0.0000 0.0032
## [13,] -0.014081172487 0.39448411 0.0000 0.0000 0.0032
## [14,] -0.004728048444 0.43587946 0.0000 0.0000 0.0012
## [15,] -0.058079904175 1.37959511 0.0000 0.0000 0.0044
## [16,] 0.001544616464 0.42371313 0.0000 0.0000 0.0020
## [17,] -0.040732695240 0.86986619 0.0000 0.0000 0.0044
## [18,] -0.006865557049 0.21533116 0.0000 0.0000 0.0024
## [19,] -0.011998894558 0.43182955 0.0000 0.0000 0.0032
## [20,] -0.008361691197 0.30970124 0.0000 0.0000 0.0028
## [21,] -0.006970104828 0.26660794 0.0000 0.0000 0.0028
## [22,] -0.007007965690 0.23325519 0.0000 0.0000 0.0016
## [23,] -0.040396262965 0.63565151 0.0000 0.0000 0.0060
## [24,] -0.020959624209 0.54080109 0.0000 0.0000 0.0024
## [25,] -0.021724730863 0.51478822 0.0000 0.0000 0.0032
## [26,] -0.005413860447 0.18892482 0.0000 0.0000 0.0016
## [27,] -0.029738397069 0.55751700 0.0000 0.0000 0.0044
## [28,] -0.023196115574 0.79488927 0.0000 0.0000 0.0028
## [29,] 0.008410026464 0.31443422 0.0000 0.0000 0.0028
## [30,] 0.005992522844 0.52089383 0.0000 0.0000 0.0036
## [31,] -0.010836618074 0.46832319 0.0000 0.0000 0.0020
## [32,] -0.019366941514 0.41092647 0.0000 0.0000 0.0040
## [33,] -0.007073964709 0.35369824 0.0000 0.0000 0.0004
## [34,] -0.009533040841 0.20545456 0.0000 0.0000 0.0024
## [35,] -0.002044884670 0.11064865 0.0000 0.0000 0.0016
## [36,] 0.017846464403 0.49706980 0.0000 0.0000 0.0032
## [37,] -0.001511884657 0.25735825 0.0000 0.0000 0.0016
## [38,] -0.000547793286 0.48696232 0.0000 0.0000 0.0032
## [39,] -0.003269810596 0.26115267 0.0000 0.0000 0.0020
## [40,] -0.004214310639 0.19912010 0.0000 0.0000 0.0024
## [41,] -0.028704990271 0.74822170 0.0000 0.0000 0.0040
## [42,] -0.015029729977 0.37392663 0.0000 0.0000 0.0032
## [43,] 0.029835510680 0.91802632 0.0000 0.0000 0.0024
## [44,] -0.017132728645 0.37365305 0.0000 0.0000 0.0032
## [45,] -0.026701494317 0.82838209 0.0000 0.0000 0.0040
## [46,] -0.020654201914 0.79934797 0.0000 0.0000 0.0032
## [47,] -0.004008427956 0.59029421 0.0000 0.0000 0.0028
## [48,] -0.029563544537 0.69968752 0.0000 0.0000 0.0032
## [49,] -0.009712658446 0.71668238 0.0000 0.0000 0.0032
## [50,] 0.005051140838 0.51037439 0.0000 0.0000 0.0028
## [51,] -0.011254438821 0.29627706 0.0000 0.0000 0.0032
## [52,] 0.003964949062 0.35243090 0.0000 0.0000 0.0020
## [53,] 0.046573381788 1.74459203 0.0000 0.0000 0.0040
## [54,] -0.007312324753 0.21243923 0.0000 0.0000 0.0024
## [55,] -0.011627855194 0.66265755 0.0000 0.0000 0.0028
## [56,] 0.010200989337 0.47201164 0.0000 0.0000 0.0024
## [57,] -0.009058233473 0.28611041 0.0000 0.0000 0.0024
## [58,] 0.012503107309 0.64921487 0.0000 0.0000 0.0028
## [59,] 0.008498426314 0.55861658 0.0000 0.0000 0.0028
## [60,] -0.013857988794 0.34216890 0.0000 0.0000 0.0032
## [61,] -0.002599128811 0.14283681 0.0000 0.0000 0.0020
## [62,] -0.033409361123 0.85233212 0.0000 0.0000 0.0036
## [63,] -0.027676783795 0.92896280 0.0000 0.0000 0.0032
## [64,] -0.000659140940 0.25364346 0.0000 0.0000 0.0020
## [65,] 0.001733394974 0.22635175 0.0000 0.0000 0.0016
## [66,] -0.007860807829 0.23076469 0.0000 0.0000 0.0016
## [67,] -0.011956818583 0.37250283 0.0000 0.0000 0.0032
## [68,] 0.000937261816 0.14082938 0.0000 0.0000 0.0020
## [69,] -0.006423707867 0.30986026 0.0000 0.0000 0.0024
## [70,] -0.017475748447 0.42127434 0.0000 0.0000 0.0024
## [71,] 0.012804709078 0.45629833 0.0000 0.0000 0.0032
## [72,] -0.001671314769 0.17985171 0.0000 0.0000 0.0016
## [73,] 0.000658612632 0.43937082 0.0000 0.0000 0.0020
## [74,] 0.017420848461 0.60014008 0.0000 0.0000 0.0016
## [75,] -0.020080414204 0.45119462 0.0000 0.0000 0.0028
## [76,] -0.008851317288 0.40565163 0.0000 0.0000 0.0032
## [77,] -0.011723376751 0.38630949 0.0000 0.0000 0.0020
## [78,] -0.041340352835 0.92628545 0.0000 0.0000 0.0060
## [79,] -0.032336387805 0.64657739 0.0000 0.0000 0.0044
## [80,] -0.025940433076 0.53424941 0.0000 0.0000 0.0044
## [81,] -0.006915207656 0.26363331 0.0000 0.0000 0.0024
## [82,] -0.016584083503 0.88943253 0.0000 0.0000 0.0020
## [83,] -0.004386522652 0.34890949 0.0000 0.0000 0.0016
## [84,] -0.005602540932 0.30335672 0.0000 0.0000 0.0020
## [85,] 0.028464118672 0.69765595 0.0000 0.0000 0.0036
## [86,] 0.002222104801 0.37119891 0.0000 0.0000 0.0056
## [87,] -0.007093243740 0.20921444 0.0000 0.0000 0.0012
## [88,] -0.004806214644 0.20942333 0.0000 0.0000 0.0024
## [89,] -0.008151481768 0.21045392 0.0000 0.0000 0.0024
## [90,] 0.001062292648 0.22314458 0.0000 0.0000 0.0016
## [91,] 0.006050744360 0.49987919 0.0000 0.0000 0.0032
## [92,] -0.009631324061 0.54801399 0.0000 0.0000 0.0012
## [93,] -0.005515533266 0.17387850 0.0000 0.0000 0.0012
## [94,] -0.002598558231 0.18080552 0.0000 0.0000 0.0020
## [95,] 0.002378794456 0.11893972 0.0000 0.0000 0.0004
## [96,] 0.013454093375 0.42284519 0.0000 0.0000 0.0028
## [97,] -0.006020974326 0.26723311 0.0000 0.0000 0.0008
## [98,] -0.007388329221 0.29598010 0.0000 0.0000 0.0016
## [99,] -0.005488423861 0.37897275 0.0000 0.0000 0.0020
## [100,] 0.000347217318 0.42933808 0.0000 0.0000 0.0016
## [101,] -0.002676813019 0.15342417 0.0000 0.0000 0.0012
## [102,] -0.005627925173 0.25175851 0.0000 0.0000 0.0024
## [103,] -0.011844692290 0.48027738 0.0000 0.0000 0.0032
## [104,] -0.001268329736 0.14999299 0.0000 0.0000 0.0016
## [105,] -0.001045182003 0.29266520 0.0000 0.0000 0.0024
## [106,] -0.008521510789 0.25306641 0.0000 0.0000 0.0036
## [107,] -0.001607109386 0.46397777 0.0000 0.0000 0.0020
## [108,] -0.002991057059 0.32306413 0.0000 0.0000 0.0012
## [109,] -0.013203907129 0.26653563 0.0000 0.0000 0.0028
## [110,] -0.006752793322 0.24854685 0.0000 0.0000 0.0020
## [111,] -0.002074205569 0.18650003 0.0000 0.0000 0.0016
## [112,] -0.008867585724 0.42849060 0.0000 0.0000 0.0032
## [113,] 0.022057077844 0.71094971 0.0000 0.0000 0.0016
## [114,] 0.009018884773 0.47724739 0.0000 0.0000 0.0020
## [115,] -0.008619826009 0.22575406 0.0000 0.0000 0.0016
## [116,] -0.017847765307 0.50532511 0.0000 0.0000 0.0060
## [117,] -0.015248694595 0.33725528 0.0000 0.0000 0.0048
## [118,] -0.000074774992 0.12451043 0.0000 0.0000 0.0012
## [119,] -0.003282572593 0.18213451 0.0000 0.0000 0.0008
## [120,] -0.003751740166 0.14635147 0.0000 0.0000 0.0012
## [121,] -0.007847722896 0.26958008 0.0000 0.0000 0.0028
## [122,] 0.006653098385 0.22623174 0.0000 0.0000 0.0016
## [123,] 0.012660124049 0.45883245 0.0000 0.0000 0.0032
## [124,] -0.019623772516 0.54933169 0.0000 0.0000 0.0032
## [125,] 0.009684540682 0.42251469 0.0000 0.0000 0.0020
## [126,] 0.008427422254 0.24225644 0.0000 0.0000 0.0036
## [127,] 0.009363123779 0.35982593 0.0000 0.0000 0.0040
## [128,] -0.005542629144 0.14901338 0.0000 0.0000 0.0020
## [129,] -0.016123626620 0.38449148 0.0000 0.0000 0.0032
## [130,] -0.001244918327 0.34023677 0.0000 0.0000 0.0016
## [131,] -0.029894041262 1.06363563 0.0000 0.0000 0.0024
## [132,] -0.004302471753 0.25635804 0.0000 0.0000 0.0020
## [133,] -0.019760522392 0.64591174 0.0000 0.0000 0.0028
## [134,] -0.000079460152 0.35183797 0.0000 0.0000 0.0020
## [135,] -0.021561690494 0.52154819 0.0000 0.0000 0.0040
## [136,] -0.010555391033 0.45399201 0.0000 0.0000 0.0032
## [137,] -0.010336818633 0.34601287 0.0000 0.0000 0.0032
## [138,] -0.012928137021 0.46364328 0.0000 0.0000 0.0032
## [139,] -0.006323032973 0.20545899 0.0000 0.0000 0.0032
## [140,] -0.018984635457 0.40891705 0.0000 0.0000 0.0040
## [141,] 0.008257402372 0.28602969 0.0000 0.0000 0.0028
## [142,] -0.017586561025 0.79359099 0.0000 0.0000 0.0020
## [143,] 0.015017855215 0.91237201 0.0000 0.0000 0.0012
## [144,] -0.013311670511 0.43429038 0.0000 0.0000 0.0028
## [145,] -0.006586659401 0.53689941 0.0000 0.0000 0.0028
## [146,] 0.003999576191 0.24275307 0.0000 0.0000 0.0016
## [147,] -0.000294332761 0.44241578 0.0000 0.0000 0.0032
## [148,] 0.005244980228 0.57523955 0.0000 0.0000 0.0032
## [149,] -0.013032968794 0.36970504 0.0000 0.0000 0.0016
## [150,] -0.003917044902 0.12556602 0.0000 0.0000 0.0020
## [151,] 0.005781301796 0.24331267 0.0000 0.0000 0.0012
## [152,] 0.284933306458 4.49136701 0.0000 0.0000 0.0076
## [153,] 0.014326929783 0.54250773 0.0000 0.0000 0.0020
## [154,] 0.047834466525 1.16532937 0.0000 0.0000 0.0044
## [155,] -0.002551890086 0.09171732 0.0000 0.0000 0.0008
## [156,] -0.021328488629 0.42952927 0.0000 0.0000 0.0032
## [157,] -0.017699617516 0.53203310 0.0000 0.0000 0.0036
## [158,] -0.012172056095 0.39001156 0.0000 0.0000 0.0016
## [159,] -0.072518520013 1.12115609 0.0000 0.0000 0.0052
## [160,] -0.049943378059 1.01841364 0.0000 0.0000 0.0044
## [161,] -0.016273023996 0.41280465 0.0000 0.0000 0.0036
## [162,] 0.001403457231 0.33030159 0.0000 0.0000 0.0020
## [163,] 0.001034070682 0.09571430 0.0000 0.0000 0.0008
## [164,] -0.002312992549 0.08391387 0.0000 0.0000 0.0012
## [165,] -0.014058402906 0.33647727 0.0000 0.0000 0.0032
## [166,] -0.024069094626 0.64577300 0.0000 0.0000 0.0036
## [167,] -0.012639900567 0.68511098 0.0000 0.0000 0.0016
## [168,] -0.057545954671 1.33160866 0.0000 0.0000 0.0048
## [169,] -0.004369740508 0.27642141 0.0000 0.0000 0.0020
## [170,] 0.000249790060 0.01033581 0.0000 0.0000 0.0008
## [171,] -0.004814476616 0.27785058 0.0000 0.0000 0.0020
## [172,] 0.003322371715 0.28304937 0.0000 0.0000 0.0024
## [173,] 0.000262044135 0.34686150 0.0000 0.0000 0.0036
## [174,] 0.000871106246 0.17484055 0.0000 0.0000 0.0016
## [175,] -0.011997385424 0.52003894 0.0000 0.0000 0.0024
## [176,] 0.000257900068 0.23451631 0.0000 0.0000 0.0016
## [177,] -0.005419969107 0.19064744 0.0000 0.0000 0.0016
## [178,] -0.005491961553 0.14912357 0.0000 0.0000 0.0016
## [179,] -0.006607039834 0.24645460 0.0000 0.0000 0.0028
## [180,] -0.029074198672 0.95631617 0.0000 0.0000 0.0052
## [181,] -0.005154792508 0.28380396 0.0000 0.0000 0.0020
## [182,] -0.005153860213 0.24098062 0.0000 0.0000 0.0020
## [183,] 0.013663074266 0.64420976 0.0000 0.0000 0.0040
## [184,] -0.011605194220 0.37096131 0.0000 0.0000 0.0052
## [185,] -0.013849934083 0.36826136 0.0000 0.0000 0.0024
## [186,] -0.006033723166 0.25128820 0.0000 0.0000 0.0028
## [187,] -0.017259157601 0.37064532 0.0000 0.0000 0.0044
## [188,] -0.003139894166 0.28067924 0.0000 0.0000 0.0040
## [189,] -0.002519755325 0.81605617 0.0000 0.0000 0.0032
## [190,] 0.008864952351 0.56598057 0.0000 0.0000 0.0040
## [191,] 0.005384770334 0.25875965 0.0000 0.0000 0.0012
## [192,] 0.007138326893 0.55395280 0.0000 0.0000 0.0020
## [193,] -0.017840666323 0.50828940 0.0000 0.0000 0.0028
## [194,] 0.001591985921 0.44204808 0.0000 0.0000 0.0028
## [195,] -0.035300528439 0.82261060 0.0000 0.0000 0.0044
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## [471,] -0.031141800176 0.80489472 0.0000 0.0000 0.0028
## [472,] -0.005892461845 0.33006215 0.0000 0.0000 0.0048
## [473,] -0.083986658901 2.63104402 0.0000 0.0000 0.0036
## [474,] -0.008533810773 0.23221115 0.0000 0.0000 0.0024
## [475,] 0.003686971151 0.78069158 0.0000 0.0000 0.0048
## [476,] -0.003163797113 0.62938739 0.0000 0.0000 0.0040
## [477,] -0.006147636056 0.27839611 0.0000 0.0000 0.0040
## [478,] -0.007780992008 0.39661424 0.0000 0.0000 0.0036
## [479,] -0.093984490440 2.33804116 0.0000 0.0000 0.0036
## [480,] -0.142000201014 3.19632623 0.0000 0.0000 0.0052
## [481,] -0.060769728387 1.80837064 0.0000 0.0000 0.0024
## [482,] 0.249961276510 5.58804373 0.0000 0.0000 0.0044
## [483,] -0.014810988996 0.56133080 0.0000 0.0000 0.0028
## [484,] -0.011618544279 0.39359184 0.0000 0.0000 0.0020
## [485,] -0.018855804139 0.78826902 0.0000 0.0000 0.0020
## [486,] -0.009757303757 0.27763284 0.0000 0.0000 0.0020
## [487,] -0.017090283849 0.49216655 0.0000 0.0000 0.0024
## [488,] 0.004925619692 0.38265231 0.0000 0.0000 0.0032
## [489,] -0.006277207751 0.26881728 0.0000 0.0000 0.0020
## [490,] -0.027915750860 0.56181334 0.0000 0.0000 0.0048
## [491,] -0.014800894443 0.50819596 0.0000 0.0000 0.0036
## [492,] -0.002319115918 0.11595580 0.0000 0.0000 0.0004
## [493,] -0.003496873201 0.32653376 0.0000 0.0000 0.0028
## [494,] 0.046835424584 1.47953993 0.0000 0.0000 0.0036
## [495,] -0.010040952447 0.32086340 0.0000 0.0000 0.0016
## [496,] -0.052951806011 1.67199012 0.0000 0.0000 0.0024
## [497,] -2.134476424506 27.89928635 0.0000 0.0000 0.0092
## [498,] 0.012077579283 0.89452195 0.0000 0.0000 0.0032
## [499,] -0.003043603448 0.18340232 0.0000 0.0000 0.0016
## [500,] 0.007856027372 1.63780425 0.0000 0.0000 0.0040
## [501,] -0.036162904540 1.26308669 0.0000 0.0000 0.0024
## [502,] -0.017105719787 0.55983922 0.0000 0.0000 0.0032
## [503,] -0.008242119569 0.30471215 0.0000 0.0000 0.0024
## [504,] -0.011749154878 0.73044559 0.0000 0.0000 0.0040
## [505,] 0.027489860471 1.49153996 0.0000 0.0000 0.0032
## [506,] -0.002752652807 1.17236117 0.0000 0.0000 0.0036
## [507,] 0.001869518856 0.22671972 0.0000 0.0000 0.0020
## [508,] -0.114474111687 3.37194109 0.0000 0.0000 0.0036
## [509,] -0.000324616770 0.66513730 0.0000 0.0000 0.0032
## [510,] -0.065670867074 1.38964905 0.0000 0.0000 0.0048
## [511,] -0.008304330869 0.33705765 0.0000 0.0000 0.0032
## [512,] -0.021027771451 0.42381202 0.0000 0.0000 0.0040
## [513,] 0.025009818260 0.88721102 0.0000 0.0000 0.0032
## [514,] -0.008749565674 0.27605469 0.0000 0.0000 0.0020
## [515,] -0.029175121261 0.98028088 0.0000 0.0000 0.0040
## [516,] -0.011105180733 1.43992925 0.0000 0.0000 0.0036
## [517,] -0.029029340105 2.03515559 0.0000 0.0000 0.0040
## [518,] 0.002121782801 0.16762617 0.0000 0.0000 0.0012
## [519,] -0.012279599003 0.48796095 0.0000 0.0000 0.0028
## [520,] -2.997726050766 32.32556987 0.0000 0.0000 0.0144
## [521,] -0.052861807069 1.80840296 0.0000 0.0000 0.0040
## [522,] 0.001908896025 0.22201078 0.0000 0.0000 0.0012
## [523,] 0.008326424483 0.86119823 0.0000 0.0000 0.0044
## [524,] -0.000696902904 0.45639412 0.0000 0.0000 0.0032
## [525,] -0.028669030127 1.03147940 0.0000 0.0000 0.0032
## [526,] -0.027864026782 1.05589509 0.0000 0.0000 0.0028
## [527,] -0.007077332746 0.35947067 0.0000 0.0000 0.0024
## [528,] -0.003165066251 0.45788826 0.0000 0.0000 0.0024
## [529,] -0.025264491998 0.73867709 0.0000 0.0000 0.0028
## [530,] -0.002407248547 0.19029916 0.0000 0.0000 0.0024
## [531,] -0.026988671900 0.79296835 0.0000 0.0000 0.0024
## [532,] -0.027904241688 0.77970081 0.0000 0.0000 0.0020
## [533,] -0.045185777690 0.90510639 0.0000 0.0000 0.0032
## [534,] -0.024288847516 0.67639589 0.0000 0.0000 0.0032
## [535,] -0.038601797467 1.82275941 0.0000 0.0000 0.0036
## [536,] -0.029216892863 0.80940221 0.0000 0.0000 0.0036
## [537,] -0.013701789131 0.40933309 0.0000 0.0000 0.0020
## [538,] 0.004075705949 0.45517398 0.0000 0.0000 0.0040
## [539,] -0.014341698543 0.96308072 0.0000 0.0000 0.0020
## [540,] -0.009575326272 0.66971146 0.0000 0.0000 0.0032
## [541,] -0.007060054628 0.28653919 0.0000 0.0000 0.0040
## [542,] -0.012043606965 0.48746361 0.0000 0.0000 0.0040
## [543,] 0.028314668300 1.78997931 0.0000 0.0000 0.0024
## [544,] 0.007813646949 0.50839276 0.0000 0.0000 0.0024
## [545,] -0.001981511014 0.33872398 0.0000 0.0000 0.0032
## [546,] -0.012736900650 1.02289589 0.0000 0.0000 0.0032
## [547,] -0.010363716157 0.52285516 0.0000 0.0000 0.0032
## [548,] -0.031452684510 0.78104597 0.0000 0.0000 0.0044
## [549,] 0.004305775664 1.36258244 0.0000 0.0000 0.0024
## [550,] -0.129130008040 2.68862453 0.0000 0.0000 0.0056
## [551,] 0.080531446342 2.55519454 0.0000 0.0000 0.0036
## [552,] -0.044850547770 0.69137476 0.0000 0.0000 0.0060
## [553,] -0.023004188346 0.73190230 0.0000 0.0000 0.0040
## [554,] -0.008586678755 0.47770567 0.0000 0.0000 0.0032
## [555,] 0.000002068235 0.07939632 0.0000 0.0000 0.0016
## [556,] -0.019235229621 1.01131797 0.0000 0.0000 0.0036
## [557,] -0.004545667809 0.14004592 0.0000 0.0000 0.0012
## [558,] -0.017375945864 0.45686944 0.0000 0.0000 0.0044
## [559,] -0.015705037547 0.32676441 0.0000 0.0000 0.0028
## [560,] -0.024787818199 0.53910394 0.0000 0.0000 0.0028
## [561,] -0.011438101184 0.72133796 0.0000 0.0000 0.0036
## [562,] -0.072383085434 1.52664383 0.0000 0.0000 0.0040
## [563,] -0.014467792585 0.69070450 0.0000 0.0000 0.0020
## [564,] -0.013353464869 0.36235357 0.0000 0.0000 0.0020
## [565,] -0.303114762368 5.43798302 0.0000 0.0000 0.0060
## [566,] 0.000726386559 0.10260490 0.0000 0.0000 0.0008
## [567,] -0.038379189583 0.98905875 0.0000 0.0000 0.0028
## [568,] -0.008404718875 0.24925761 0.0000 0.0000 0.0028
## [569,] -0.048219126132 1.39119417 0.0000 0.0000 0.0028
## [570,] -0.002457785742 0.52866129 0.0000 0.0000 0.0040
## [571,] -0.102958272408 2.38990795 0.0000 0.0000 0.0040
## [572,] -0.019193101806 1.34281231 0.0000 0.0000 0.0032
## [573,] -0.396076693746 5.78309796 0.0000 0.0000 0.0092
## [574,] -0.006313014750 0.41562784 0.0000 0.0000 0.0024
## [575,] -0.033720494551 0.94647386 0.0000 0.0000 0.0036
## [576,] -0.011152609663 0.31138895 0.0000 0.0000 0.0040
## [577,] -0.013059316532 0.61140019 0.0000 0.0000 0.0016
## [578,] -0.100127876897 2.41655345 0.0000 0.0000 0.0048
## [579,] -0.008973082135 0.39429415 0.0000 0.0000 0.0044
## [580,] -0.011030843931 0.26967397 0.0000 0.0000 0.0024
## [581,] -0.201728789034 3.27176164 0.0000 0.0000 0.0064
## [582,] -0.041803502023 1.28385285 0.0000 0.0000 0.0032
## [583,] -0.097971804684 1.67550962 0.0000 0.0000 0.0072
## [584,] -0.006987558911 0.20523184 0.0000 0.0000 0.0016
## [585,] -0.006130884904 0.30916311 0.0000 0.0000 0.0016
## [586,] -0.042517441424 1.09125098 0.0000 0.0000 0.0028
## [587,] -0.040261410417 1.49989696 0.0000 0.0000 0.0024
## [588,] -0.003070691183 0.22089697 0.0000 0.0000 0.0024
## [589,] -0.018134767918 0.60141194 0.0000 0.0000 0.0028
## [590,] -0.011828056074 0.34018718 0.0000 0.0000 0.0024
## [591,] -0.010603148848 0.36074802 0.0000 0.0000 0.0040
## [592,] -0.126385116105 3.19453967 0.0000 0.0000 0.0048
## [593,] 0.004346256392 0.29474449 0.0000 0.0000 0.0028
## [594,] 0.001607894761 0.86622374 0.0000 0.0000 0.0036
## [595,] -0.006843810579 0.27519376 0.0000 0.0000 0.0036
## [596,] -0.213985355554 3.97810615 0.0000 0.0000 0.0060
## [597,] 0.103239089171 2.44129021 0.0000 0.0000 0.0036
## [598,] -0.033178388236 1.34579511 0.0000 0.0000 0.0028
## [599,] -0.018999757210 0.48023082 0.0000 0.0000 0.0044
## [600,] -0.020688925033 0.95490308 0.0000 0.0000 0.0028
## [601,] 0.001052383986 0.17934720 0.0000 0.0000 0.0020
## [602,] -0.000543938060 0.03789731 0.0000 0.0000 0.0008
## [603,] -0.006890501416 0.23812849 0.0000 0.0000 0.0012
## [604,] -0.024701774100 0.84993751 0.0000 0.0000 0.0032
## [605,] -0.018436160595 0.50035996 0.0000 0.0000 0.0020
## [606,] -0.032711158116 0.77386803 0.0000 0.0000 0.0028
## [607,] -0.033769528409 0.93590009 0.0000 0.0000 0.0052
## [608,] 0.016533695553 0.88303353 0.0000 0.0000 0.0028
## [609,] -0.017040950331 0.72590279 0.0000 0.0000 0.0040
## [610,] -0.000075473388 0.23066715 0.0000 0.0000 0.0020
## [611,] -0.044911236588 1.00893242 0.0000 0.0000 0.0040
## [612,] -0.207377264934 6.62336792 0.0000 0.0000 0.0020
## [613,] -0.015633233961 0.36642989 0.0000 0.0000 0.0028
## [614,] -0.014466193983 0.48746437 0.0000 0.0000 0.0028
## [615,] -0.009470066567 0.19916754 0.0000 0.0000 0.0028
## [616,] -0.011145309563 0.34862780 0.0000 0.0000 0.0016
## [617,] -0.073694412234 2.01949504 0.0000 0.0000 0.0040
## [618,] -0.002270744493 0.51013186 0.0000 0.0000 0.0024
## [619,] -0.051986057943 1.76236121 0.0000 0.0000 0.0040
## [620,] 0.341216508777 4.97323382 0.0000 0.0000 0.0068
## [621,] -0.029057316208 1.20740489 0.0000 0.0000 0.0044
## [622,] -0.004170036862 0.25888583 0.0000 0.0000 0.0036
## [623,] -0.016762095999 0.40390086 0.0000 0.0000 0.0044
## [624,] -0.008841936632 0.55027973 0.0000 0.0000 0.0020
## [625,] -0.039895625749 0.86854427 0.0000 0.0000 0.0036
## [626,] -0.020756836968 0.44238837 0.0000 0.0000 0.0032
## [627,] -0.091342617027 2.25213631 0.0000 0.0000 0.0052
## [628,] -0.021496827341 0.52338538 0.0000 0.0000 0.0044
## [629,] -0.031196556951 0.81346827 0.0000 0.0000 0.0040
## [630,] -0.009783985344 0.46546275 0.0000 0.0000 0.0040
## [631,] -0.004560723218 0.23887607 0.0000 0.0000 0.0016
## [632,] 0.022300146074 1.50436254 0.0000 0.0000 0.0012
## [633,] -0.032713580312 0.92275375 0.0000 0.0000 0.0028
## [634,] -0.071150894745 1.35655854 0.0000 0.0000 0.0052
## [635,] 0.038541260512 3.00516041 0.0000 0.0000 0.0040
## [636,] -0.007490317427 0.28593387 0.0000 0.0000 0.0032
## [637,] -0.008985082498 0.31613161 0.0000 0.0000 0.0020
## [638,] -0.006528229600 0.37584409 0.0000 0.0000 0.0032
## [639,] 0.005332243328 1.28345259 0.0000 0.0000 0.0036
## [640,] -0.013339265053 0.54098719 0.0000 0.0000 0.0024
## [641,] 0.007569581779 0.41217586 0.0000 0.0000 0.0036
## [642,] -0.364544301470 5.57496331 0.0000 0.0000 0.0088
## [643,] 0.804756106851 9.42468385 0.0000 0.0000 0.0120
## [644,] -0.036964913415 1.46315369 0.0000 0.0000 0.0032
## [645,] -0.000739854426 0.04456326 0.0000 0.0000 0.0012
## [646,] -0.007641471135 0.35127714 0.0000 0.0000 0.0032
## [647,] -0.020616237369 0.80490443 0.0000 0.0000 0.0048
## [648,] -0.050242804962 1.30316383 0.0000 0.0000 0.0036
## [649,] -0.008910899720 0.32236444 0.0000 0.0000 0.0032
## [650,] -0.035852563233 0.83401858 0.0000 0.0000 0.00363.4.4 Predict fitted values for each individual
pred.npb3 <- predict(fit.npb3)
fittedvals3 <- pred.npb3$fitted.vals3.4.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals3, Y)
abline(a = 0, b = 1, col = "red")
3.5 Fit the NPB model without ozone and without temperature
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone or temperature just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb4 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2,3)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb4, file = here::here("Results", "NPB_Birth_Weight_v4a.4.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.4.rdata"))
npb.sum4 <- summary(fit.npb4)3.5.1 First, main effect regression coefficients with PIPs
rownames(npb.sum4$main.effects) <- colnames(X.scaled[,-c(2,3)])
npb.sum4$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm 0.01740483 6.666825 -13.66354 16.261833 0.2588
## pct_tree_cover -0.42808738 6.557343 -16.07193 14.870785 0.2664
## pct_impervious -2.98242948 8.784403 -29.50467 8.315785 0.3316
## mean_aadt_intensity -0.33582811 5.719151 -12.95181 13.143332 0.2432
## dist_m_tri -0.32784261 6.267080 -15.15440 14.480333 0.2580
## dist_m_npl 0.32661062 6.933992 -13.35060 18.758868 0.2620
## dist_m_waste_site 1.74392766 8.859841 -10.75379 29.415047 0.2868
## dist_m_major_emit -0.09948045 5.647990 -12.23102 13.491529 0.2452
## dist_m_cafo -3.47107470 17.884937 -52.96240 17.467822 0.3368
## dist_m_mine_well -2.78266572 9.539020 -30.03867 10.711788 0.3192
## cvd_rate_adj -3.05062600 9.576883 -30.91481 9.044841 0.3148
## res_rate_adj -2.30442258 8.327439 -24.91180 8.452087 0.3104
## violent_crime_rate -0.21414248 6.094327 -13.88438 13.958877 0.2600
## property_crime_rate -1.18082454 6.079274 -17.81515 10.538959 0.2608
## pct_less_hs -1.68535722 8.358050 -22.33047 12.282048 0.2988
## pct_unemp -21.61340643 27.288321 -85.60404 0.000000 0.6404
## pct_limited_eng -1.54816907 7.169160 -21.28668 11.274985 0.3024
## pct_hh_pov -0.82644993 7.254424 -16.95409 13.457831 0.2788
## pct_poc -1.26695546 8.277818 -21.24654 13.978007 0.29763.5.2 Next, posterior means and CIs for covariates
rownames(npb.sum4$covariates)[2:nrow(npb.sum4$covariates)] <- colnames(W.scaled2)
npb.sum4$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3082.964159 218.31444 2666.165179 3496.98883
## lat -9.514005 325.52873 -657.187948 635.18284
## lon 12.764785 155.28519 -294.162668 318.36380
## lat_lon_int 1.435636 394.32695 -788.038926 775.75827
## ed_no_hs 111.713087 77.30533 -41.633044 265.05261
## ed_hs 66.647739 70.85823 -70.204042 205.63410
## ed_aa 15.575205 60.57621 -103.141967 133.62891
## ed_4yr 59.803128 52.88785 -42.903199 165.34836
## low_bmi -105.463024 94.74011 -288.888479 76.96030
## ovwt_bmi 31.081805 41.20973 -47.859949 112.26486
## obese_bmi 99.227241 47.07821 4.635381 192.13086
## concep_spring -38.795879 49.07741 -136.048470 55.15986
## concep_summer 65.600579 49.62205 -30.973515 164.08209
## concep_fall 68.940271 47.98050 -26.548434 163.50593
## concep_2010 -4.802284 216.03491 -424.271817 408.52731
## concep_2011 -24.535652 215.19071 -434.143224 384.80841
## concep_2012 -54.791861 214.74605 -468.629692 366.34955
## concep_2013 67.670824 215.49603 -345.352147 478.39258
## maternal_age 81.054147 22.47691 36.460698 124.78256
## any_smoker -146.697446 64.40336 -270.919548 -20.62775
## smokeSH -114.234422 45.04711 -202.917718 -29.30478
## mean_cpss 12.594717 20.40150 -27.405490 51.69029
## mean_epsd -53.324959 20.66938 -93.707931 -13.08126
## male 157.246918 34.33731 89.717584 222.695473.5.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum4$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.0535398565 0.8554814 0 0 0.0124
## [2,] -0.0277599988 0.5874716 0 0 0.0104
## [3,] 0.0255571941 1.1632129 0 0 0.0124
## [4,] -0.0357963402 0.8616498 0 0 0.0128
## [5,] -0.0355543254 0.6103949 0 0 0.0104
## [6,] -0.0688209405 1.3881109 0 0 0.0116
## [7,] -0.0445171591 0.6889427 0 0 0.0104
## [8,] -0.1378766561 1.7597244 0 0 0.0176
## [9,] -0.0289782465 0.6063844 0 0 0.0108
## [10,] -0.0336587894 1.0159475 0 0 0.0132
## [11,] -0.0233540581 0.4725086 0 0 0.0096
## [12,] -0.0494650615 0.7213515 0 0 0.0124
## [13,] -0.0454922259 0.8267308 0 0 0.0120
## [14,] -0.0740927258 1.1672629 0 0 0.0116
## [15,] -0.0385564524 0.5806577 0 0 0.0096
## [16,] -0.0820598624 1.0611379 0 0 0.0180
## [17,] -0.0061676447 0.3968900 0 0 0.0088
## [18,] -0.0252153623 0.9371627 0 0 0.0152
## [19,] 0.0281696484 0.8763174 0 0 0.0104
## [20,] -0.0081305603 0.8165736 0 0 0.0112
## [21,] 0.0012292995 0.7253463 0 0 0.0148
## [22,] -0.0920894663 1.2864090 0 0 0.0168
## [23,] -0.0042069433 0.6677543 0 0 0.0112
## [24,] 0.0377529265 0.9537081 0 0 0.0088
## [25,] -0.0302423366 0.5688879 0 0 0.0108
## [26,] -0.0750717333 1.2152646 0 0 0.0144
## [27,] 0.0071106223 0.7592570 0 0 0.0092
## [28,] -0.0147856077 0.8315756 0 0 0.0108
## [29,] -0.0277397628 0.6986635 0 0 0.0096
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## [354,] -0.0252662461 0.5031216 0 0 0.0120
## [355,] -0.0047883097 1.0391818 0 0 0.0172
## [356,] 0.0022405328 0.6223445 0 0 0.0092
## [357,] 0.0048555457 0.7321943 0 0 0.0100
## [358,] -0.0301534320 1.0456127 0 0 0.0132
## [359,] 0.0782300797 2.9092308 0 0 0.0112
## [360,] -0.0941389368 1.7878229 0 0 0.0164
## [361,] -0.0163216579 0.6968084 0 0 0.0108
## [362,] -0.0587139234 0.9708574 0 0 0.0124
## [363,] -0.1395803037 3.3610443 0 0 0.0116
## [364,] -0.0406331318 1.8686695 0 0 0.0172
## [365,] -0.0267283241 0.7827867 0 0 0.0128
## [366,] -0.0699290075 1.2529449 0 0 0.0144
## [367,] -0.0114237773 0.6008901 0 0 0.0108
## [368,] 0.0446564944 1.8279960 0 0 0.0136
## [369,] -0.0029104968 1.9623826 0 0 0.0140
## [370,] 0.0851744271 2.8007365 0 0 0.0100
## [371,] -0.0773573571 1.3458747 0 0 0.0156
## [372,] -0.0629260725 1.2682154 0 0 0.0144
## [373,] -0.0164903318 0.6054618 0 0 0.0184
## [374,] -0.1846699042 5.7855249 0 0 0.0172
## [375,] -0.0938309275 1.8117557 0 0 0.0132
## [376,] -0.0314303452 0.6162595 0 0 0.0092
## [377,] -0.0221551492 0.5309392 0 0 0.0112
## [378,] -0.0827136214 1.4309522 0 0 0.0164
## [379,] 0.0335127316 1.1778972 0 0 0.0108
## [380,] 0.0233813409 1.1260255 0 0 0.0148
## [381,] -0.0484931523 0.9830387 0 0 0.0116
## [382,] -0.0199669857 1.0938196 0 0 0.0120
## [383,] -0.0775153575 1.2548619 0 0 0.0132
## [384,] -0.0121156745 1.1218298 0 0 0.0144
## [385,] 0.0179515081 0.7787999 0 0 0.0144
## [386,] -0.1357247010 3.1202231 0 0 0.0136
## [387,] -0.0368310721 0.8046809 0 0 0.0104
## [388,] -0.0257300141 0.7500180 0 0 0.0148
## [389,] -0.0238558322 1.0594992 0 0 0.0144
## [390,] -0.1349818732 2.2564102 0 0 0.0176
## [391,] -0.0069666122 1.3060318 0 0 0.0140
## [392,] -0.0215410619 0.8868134 0 0 0.0108
## [393,] 0.0995894170 2.0930555 0 0 0.0132
## [394,] -1.1714819237 10.4477363 0 0 0.0240
## [395,] -0.0311524954 0.5946701 0 0 0.0096
## [396,] -0.0176219728 0.8045246 0 0 0.0112
## [397,] -0.0120140792 0.6400092 0 0 0.0096
## [398,] -0.0496533167 0.9123524 0 0 0.0140
## [399,] 0.0102881505 0.8829526 0 0 0.0128
## [400,] -0.0006675648 0.5233028 0 0 0.0108
## [401,] -0.0985334889 1.6598146 0 0 0.0128
## [402,] -0.0244185339 0.6695409 0 0 0.0092
## [403,] -0.0403133383 0.7566425 0 0 0.0100
## [404,] -0.0297759989 0.4725258 0 0 0.0096
## [405,] -0.1134107912 2.2823800 0 0 0.0144
## [406,] -0.0766191975 2.0847773 0 0 0.0132
## [407,] -0.0347050479 0.7122233 0 0 0.0120
## [408,] -0.1810995916 3.0366084 0 0 0.0192
## [409,] -0.0555759544 1.4045868 0 0 0.0112
## [410,] -0.0306577138 0.9934268 0 0 0.0132
## [411,] -0.0127761897 1.2176525 0 0 0.0112
## [412,] -0.0439581904 0.9275935 0 0 0.0088
## [413,] -0.0517067746 1.0478064 0 0 0.0164
## [414,] -0.1478757742 2.4749427 0 0 0.0136
## [415,] -0.0885330640 1.6671236 0 0 0.0140
## [416,] -0.1007692644 1.3503364 0 0 0.0180
## [417,] 0.3287193528 4.8175565 0 0 0.0172
## [418,] -0.0491135236 0.6689021 0 0 0.0128
## [419,] -0.0085869778 0.5587601 0 0 0.0080
## [420,] -0.0954179125 1.5290524 0 0 0.0128
## [421,] -0.0337360837 0.8448320 0 0 0.0148
## [422,] -0.0273252074 0.5335315 0 0 0.0120
## [423,] -0.0190790470 0.7921363 0 0 0.0112
## [424,] -0.0553627189 0.9803798 0 0 0.0152
## [425,] -0.0495417451 1.5055328 0 0 0.0124
## [426,] -0.0291552692 0.7651675 0 0 0.0132
## [427,] -0.0309927087 0.6889990 0 0 0.0144
## [428,] -0.0385158566 0.6403777 0 0 0.0144
## [429,] -0.0160177130 0.8299958 0 0 0.0128
## [430,] -0.0259135005 0.7854044 0 0 0.0116
## [431,] -0.1820848454 2.8136124 0 0 0.0168
## [432,] -0.1356626636 3.1914046 0 0 0.0156
## [433,] -0.0041779944 1.0952521 0 0 0.0128
## [434,] -0.0323654519 0.5779149 0 0 0.0092
## [435,] -0.0591659080 1.2820509 0 0 0.0104
## [436,] -0.0025565029 0.9469463 0 0 0.0152
## [437,] -0.0729572413 1.0439326 0 0 0.0184
## [438,] -0.1297239181 2.3323048 0 0 0.0152
## [439,] -0.0658152462 1.2009247 0 0 0.0108
## [440,] 0.1347551550 2.7653624 0 0 0.0148
## [441,] -0.0421663180 0.7411528 0 0 0.0112
## [442,] 0.0084089201 0.7559332 0 0 0.0136
## [443,] -0.1130573559 2.2377182 0 0 0.0140
## [444,] -0.0352913258 0.8514778 0 0 0.0112
## [445,] -0.0101461515 0.4857774 0 0 0.0112
## [446,] -0.0224797526 0.8747943 0 0 0.0120
## [447,] -0.0548945762 1.3985419 0 0 0.0108
## [448,] -0.0483941876 0.9678491 0 0 0.0148
## [449,] -0.0389438185 0.7818459 0 0 0.0136
## [450,] -0.0304748501 0.5744277 0 0 0.0124
## [451,] -0.0563976487 0.8879204 0 0 0.0172
## [452,] -0.0012804096 0.8564892 0 0 0.0132
## [453,] -0.0119999067 0.7183194 0 0 0.0140
## [454,] -0.0741645113 1.4937353 0 0 0.0120
## [455,] -0.4454253112 10.5309020 0 0 0.0188
## [456,] -0.0606741732 2.0292095 0 0 0.0112
## [457,] 0.0311903860 1.4087364 0 0 0.0108
## [458,] -0.0150267528 0.7463461 0 0 0.0104
## [459,] 0.0089377035 0.8801013 0 0 0.0140
## [460,] -0.0239324365 0.6449306 0 0 0.0116
## [461,] -0.0409116413 1.4992657 0 0 0.0160
## [462,] -0.0510436686 0.7730598 0 0 0.0128
## [463,] 0.0456263225 1.8046072 0 0 0.0152
## [464,] -0.0053270123 0.7762664 0 0 0.0120
## [465,] -0.0089377960 1.0687123 0 0 0.0116
## [466,] -0.0698618894 1.8185994 0 0 0.0128
## [467,] 0.0044727925 0.7532355 0 0 0.0104
## [468,] -0.1574219545 2.4578308 0 0 0.0172
## [469,] -0.0528057283 0.9004905 0 0 0.0152
## [470,] -0.0519656288 0.8886719 0 0 0.0136
## [471,] -0.0326272174 1.1316875 0 0 0.0092
## [472,] -0.0097075499 0.5883777 0 0 0.0136
## [473,] -0.0041254381 0.6858135 0 0 0.0124
## [474,] -0.0144803501 0.6596757 0 0 0.0076
## [475,] -0.0281200664 0.9066350 0 0 0.0104
## [476,] -0.0235500929 1.0726064 0 0 0.0116
## [477,] -0.0355699628 1.0010247 0 0 0.0120
## [478,] -0.3199229738 8.1957864 0 0 0.0152
## [479,] -0.0712927583 1.4738917 0 0 0.0116
## [480,] 0.0047483816 0.8533652 0 0 0.0104
## [481,] -0.0157251729 0.6220371 0 0 0.0088
## [482,] -0.0315544937 0.7884933 0 0 0.0112
## [483,] -0.1025589032 2.3039044 0 0 0.0120
## [484,] -0.0520991204 1.7932099 0 0 0.0116
## [485,] -0.0252776714 1.1420361 0 0 0.0160
## [486,] -0.0223240688 1.0785619 0 0 0.0132
## [487,] -0.0502296836 1.2151220 0 0 0.0084
## [488,] -0.0068791980 0.6631706 0 0 0.0152
## [489,] -0.0543707585 0.9019724 0 0 0.0112
## [490,] -0.0149060875 0.6401027 0 0 0.0132
## [491,] -0.1196036458 2.0826305 0 0 0.0176
## [492,] -0.0303435198 0.8253081 0 0 0.0096
## [493,] -0.0134987247 0.7442187 0 0 0.0112
## [494,] -0.0263858828 0.5475027 0 0 0.0072
## [495,] -0.1139105649 1.8465774 0 0 0.0164
## [496,] -0.0345007499 0.6768059 0 0 0.0140
## [497,] -0.0215312032 2.9983844 0 0 0.0164
## [498,] -0.0169193440 1.4698842 0 0 0.0124
## [499,] -0.0503516377 1.3143852 0 0 0.0152
## [500,] -0.0702099796 2.0673410 0 0 0.0120
## [501,] -0.0793586130 1.7850180 0 0 0.0136
## [502,] -0.0045875219 0.5393403 0 0 0.0104
## [503,] -0.0284422397 0.9856570 0 0 0.0112
## [504,] -0.0579015665 1.5494622 0 0 0.0108
## [505,] 0.0001927488 1.0962692 0 0 0.0116
## [506,] -0.0562989899 1.2854899 0 0 0.0116
## [507,] -0.0101133980 1.0184602 0 0 0.0128
## [508,] -0.1706100548 2.6925370 0 0 0.0176
## [509,] 0.0487431949 1.6508168 0 0 0.0128
## [510,] -0.1388462448 2.5711944 0 0 0.0180
## [511,] -0.0352051982 0.6776727 0 0 0.0116
## [512,] -0.0354814760 1.0049941 0 0 0.0124
## [513,] 0.0227524025 1.1172539 0 0 0.0132
## [514,] -0.0218979384 0.4156544 0 0 0.0088
## [515,] 0.0011531605 0.5217240 0 0 0.0092
## [516,] -0.0434169327 0.7402442 0 0 0.0148
## [517,] -0.0295150253 1.1993905 0 0 0.0172
## [518,] -0.1227369855 1.7160016 0 0 0.0164
## [519,] -0.0399775866 0.7252686 0 0 0.0124
## [520,] -0.1621839842 2.9586232 0 0 0.0168
## [521,] -0.0239417136 0.7770905 0 0 0.0152
## [522,] -0.0841600467 1.7071529 0 0 0.0148
## [523,] -0.3316423080 4.1672280 0 0 0.0160
## [524,] -0.0594682333 1.4186603 0 0 0.0180
## [525,] -0.1338299417 2.4915369 0 0 0.0152
## [526,] -0.0387584337 0.8415752 0 0 0.0152
## [527,] -0.0592852799 1.2188360 0 0 0.0144
## [528,] -0.0342811977 0.7509679 0 0 0.0176
## [529,] -0.3902011787 5.0841336 0 0 0.0192
## [530,] -0.0603723117 0.9080311 0 0 0.0120
## [531,] -0.3785734122 4.9994501 0 0 0.0172
## [532,] -0.0018561321 0.7034875 0 0 0.0116
## [533,] -0.0436524285 1.2053423 0 0 0.0120
## [534,] -0.0413731049 0.7968729 0 0 0.0120
## [535,] -0.1676153514 3.8199016 0 0 0.0156
## [536,] -0.1875010569 3.1558497 0 0 0.0144
## [537,] -0.0521748161 0.9359901 0 0 0.0104
## [538,] -0.0180576172 0.5358664 0 0 0.0140
## [539,] -0.8309176440 7.8545148 0 0 0.0292
## [540,] -0.1404784561 2.4221056 0 0 0.0148
## [541,] -0.2670581529 3.3141116 0 0 0.0192
## [542,] -0.0530849319 0.7421441 0 0 0.0116
## [543,] -0.0565601953 1.1184321 0 0 0.0152
## [544,] 0.0096006952 0.8199066 0 0 0.0092
## [545,] -0.1448135955 2.5292983 0 0 0.0168
## [546,] -0.0604285155 1.6669877 0 0 0.0128
## [547,] -0.0307996786 1.2351688 0 0 0.0144
## [548,] -0.0169982953 0.6369654 0 0 0.0112
## [549,] 0.0042088282 0.9711590 0 0 0.0104
## [550,] -0.1058490803 1.5195280 0 0 0.0140
## [551,] -0.0237602173 0.7940822 0 0 0.0116
## [552,] -0.0253231444 1.8885887 0 0 0.0132
## [553,] -0.0154763632 0.7991267 0 0 0.0120
## [554,] -0.1589847457 1.8586019 0 0 0.0204
## [555,] 0.0158796288 1.0103572 0 0 0.0136
## [556,] -0.1025583126 2.5698655 0 0 0.0128
## [557,] -0.0071940594 0.4700438 0 0 0.0104
## [558,] -0.0543211723 1.6323820 0 0 0.0136
## [559,] -0.0163938623 0.9459970 0 0 0.0108
## [560,] -0.0323444499 0.5378742 0 0 0.0084
## [561,] -0.0239963840 0.8501048 0 0 0.0128
## [562,] -0.0333813087 0.9014754 0 0 0.0100
## [563,] -0.0012151227 0.8015779 0 0 0.0096
## [564,] -0.1421990748 2.2553920 0 0 0.0156
## [565,] -0.0928661966 1.4907297 0 0 0.0168
## [566,] 0.0011348669 1.0296102 0 0 0.0092
## [567,] 0.0101763584 1.0693678 0 0 0.0152
## [568,] -0.0586740331 1.1111645 0 0 0.0132
## [569,] -0.0684125029 1.2679190 0 0 0.0108
## [570,] -0.1171469421 2.1579338 0 0 0.0120
## [571,] -0.0273887135 0.5841025 0 0 0.0080
## [572,] 0.0026318322 1.0076667 0 0 0.0092
## [573,] -0.0426927657 0.7401675 0 0 0.0128
## [574,] -0.0038601525 0.8015268 0 0 0.0124
## [575,] -0.0960533659 1.7560535 0 0 0.0136
## [576,] -0.0467252421 1.1956374 0 0 0.0132
## [577,] -0.0635958162 1.5575722 0 0 0.0096
## [578,] 0.2653361117 4.2502310 0 0 0.0164
## [579,] -0.1001262265 2.4042200 0 0 0.0120
## [580,] -0.0298604533 1.0531657 0 0 0.0140
## [581,] -0.1457337210 2.9160920 0 0 0.0116
## [582,] 0.0151159682 1.3015951 0 0 0.0096
## [583,] -0.0531626298 0.6824881 0 0 0.0136
## [584,] -0.0238795571 0.8771228 0 0 0.0124
## [585,] -0.0805775292 1.3170263 0 0 0.0156
## [586,] -0.0352694022 0.7153470 0 0 0.0140
## [587,] -0.1278110778 1.4612132 0 0 0.0164
## [588,] -0.0585217288 1.3671481 0 0 0.0100
## [589,] -0.0537305557 1.2121609 0 0 0.0132
## [590,] 0.0497467631 2.0005320 0 0 0.0100
## [591,] -0.0364791537 0.9034047 0 0 0.0164
## [592,] -0.1214194993 2.0566505 0 0 0.0180
## [593,] -0.1129100161 2.5673314 0 0 0.0164
## [594,] -0.0167547914 0.4065176 0 0 0.0112
## [595,] -0.0600656663 2.2413575 0 0 0.0136
## [596,] -0.0731911175 1.7236169 0 0 0.0124
## [597,] -0.0022971184 0.9686253 0 0 0.0128
## [598,] -0.1751888479 3.4273102 0 0 0.0156
## [599,] -0.0276795540 0.8566947 0 0 0.0112
## [600,] -0.4735701251 6.5896271 0 0 0.0200
## [601,] 0.4192674309 5.9960167 0 0 0.0180
## [602,] -0.0787735480 1.7553057 0 0 0.0132
## [603,] -0.0332669479 0.8107603 0 0 0.0100
## [604,] -0.0831124467 2.2230469 0 0 0.0152
## [605,] -0.0062627532 0.8298027 0 0 0.0096
## [606,] -0.0782849945 1.2650414 0 0 0.0112
## [607,] -0.0560609597 0.7830587 0 0 0.0148
## [608,] -0.0234426753 0.6803685 0 0 0.01163.5.4 Predict fitted values for each individual
pred.npb4 <- predict(fit.npb4)
fittedvals4 <- pred.npb4$fitted.vals3.5.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals4, Y)
abline(a = 0, b = 1, col = "red")
4 Linear model with the ozone and temperature predictors
The standard deviation of the mean_o3 variable is 3.06 ppb The standard deviation of the mean_temp variable is 4.54 degrees F
lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"#names(lm_df)[2] <- "mean_o3"
head(lm_df)bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = lm_df)
summary(bw_lm)##
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp +
## lat + lon + lat_lon_int + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1916.84 -299.83 22.74 322.87 1452.55
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2930.492 491.139 5.967 0.00000000352 ***
## mean_o3 -111.268 54.733 -2.033 0.042364 *
## mean_temp 84.994 54.223 1.568 0.117361
## lat -5567.372 17614.332 -0.316 0.752025
## lon 2639.415 8294.781 0.318 0.750408
## lat_lon_int -6721.801 21280.722 -0.316 0.752182
## ed_no_hs 89.580 72.416 1.237 0.216416
## ed_hs 64.452 64.814 0.994 0.320305
## ed_aa 11.513 57.570 0.200 0.841537
## ed_4yr 73.862 50.607 1.460 0.144782
## low_bmi -91.668 92.115 -0.995 0.319944
## ovwt_bmi 34.637 39.873 0.869 0.385256
## obese_bmi 111.890 45.156 2.478 0.013406 *
## concep_spring -140.315 58.043 -2.417 0.015835 *
## concep_summer -68.668 75.272 -0.912 0.361883
## concep_fall 20.815 72.159 0.288 0.773063
## concep_2010 279.892 492.161 0.569 0.569706
## concep_2011 272.096 493.065 0.552 0.581196
## concep_2012 380.688 495.399 0.768 0.442430
## concep_2013 367.451 492.442 0.746 0.455759
## maternal_age 73.144 21.736 3.365 0.000799 ***
## any_smoker -165.074 62.974 -2.621 0.008912 **
## smokeSH -82.686 43.786 -1.888 0.059301 .
## mean_cpss 8.597 19.625 0.438 0.661458
## mean_epsd -49.574 19.979 -2.481 0.013280 *
## male 169.917 32.395 5.245 0.00000019614 ***
## mean_o3:mean_temp -153.026 16.805 -9.106 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 478.6 on 870 degrees of freedom
## Multiple R-squared: 0.198, Adjusted R-squared: 0.1741
## F-statistic: 8.263 on 26 and 870 DF, p-value: < 0.00000000000000022plot(bw_lm)## Warning: not plotting observations with leverage one:
## 1
5 Try a GAM with the ozone and temperature predictor
The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone to see about potential nonlinear effects
library(mgcv)## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.library(tidymv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"#names(gam_df)[2] <- "mean_o3"
head(gam_df)bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df, method = "REML")
summary(bw_gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2643.384 470.694 5.616 0.0000000265 ***
## lat -3294.013 16926.563 -0.195 0.84575
## lon 1573.699 7971.155 0.197 0.84354
## lat_lon_int -3979.412 20449.817 -0.195 0.84576
## ed_no_hs 63.422 69.324 0.915 0.36052
## ed_hs 39.186 62.319 0.629 0.52965
## ed_aa 13.279 55.127 0.241 0.80970
## ed_4yr 65.191 48.430 1.346 0.17863
## low_bmi -132.488 88.226 -1.502 0.13355
## ovwt_bmi 47.005 38.220 1.230 0.21909
## obese_bmi 97.096 43.301 2.242 0.02519 *
## concep_spring -100.337 63.277 -1.586 0.11318
## concep_summer -191.433 93.314 -2.051 0.04052 *
## concep_fall -56.565 91.389 -0.619 0.53611
## concep_2010 513.215 474.895 1.081 0.28014
## concep_2011 451.332 475.951 0.948 0.34326
## concep_2012 633.958 477.744 1.327 0.18487
## concep_2013 572.489 475.387 1.204 0.22882
## maternal_age 76.051 20.794 3.657 0.00027 ***
## any_smoker -169.774 60.221 -2.819 0.00493 **
## smokeSH -70.957 41.769 -1.699 0.08972 .
## mean_cpss 7.023 18.856 0.372 0.70966
## mean_epsd -48.229 19.127 -2.521 0.01187 *
## male 153.527 30.962 4.959 0.0000008571 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 20.43 25.18 7.548 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.258 Deviance explained = 29.4%
## -REML = 6643.9 Scale est. = 2.0583e+05 n = 897library(mgcViz)## Loading required package: qgam## Loading required package: rgl## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## Registered S3 method overwritten by 'mgcViz':
## method from
## +.gg GGally##
## Attaching package: 'mgcViz'## The following objects are masked from 'package:stats':
##
## qqline, qqnorm, qqplotgam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4a.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500) 6 GAM Sensitivity Analysis
The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.
Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 5% of data and just use the middle 90%.
library(mgcv)
quantile(X.scaled[,"mean_o3"], probs = c(0.05, 0.95))## 5% 95%
## -1.568529 1.633168q_5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.05))
q_95 <- quantile(X.scaled[,"mean_o3"], probs = c(0.95))
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"head(gam_df)gam_df2 <- gam_df %>%
filter(mean_o3 > q_5 & mean_o3 < q_95)
hist(gam_df2$mean_o3)
bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df2, method = "REML")
summary(bw_gam2)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2693.68 467.02 5.768 0.0000000116 ***
## lat 1830.07 17945.23 0.102 0.918799
## lon -854.75 8450.03 -0.101 0.919455
## lat_lon_int 2217.23 21680.13 0.102 0.918569
## ed_no_hs 79.02 72.18 1.095 0.274013
## ed_hs 48.58 64.37 0.755 0.450659
## ed_aa 34.44 57.29 0.601 0.547899
## ed_4yr 41.57 50.41 0.825 0.409820
## low_bmi -186.22 90.69 -2.053 0.040362 *
## ovwt_bmi 36.73 39.67 0.926 0.354802
## obese_bmi 87.89 45.55 1.930 0.054020 .
## concep_spring -63.02 66.02 -0.955 0.340076
## concep_summer -133.86 91.72 -1.459 0.144875
## concep_fall -46.95 88.85 -0.528 0.597310
## concep_2010 506.97 470.51 1.077 0.281602
## concep_2011 467.51 471.84 0.991 0.322077
## concep_2012 552.20 473.86 1.165 0.244242
## concep_2013 552.50 471.32 1.172 0.241463
## maternal_age 77.68 21.73 3.574 0.000374 ***
## any_smoker -216.85 61.92 -3.502 0.000488 ***
## smokeSH -70.67 43.61 -1.621 0.105513
## mean_cpss 13.86 19.71 0.703 0.482190
## mean_epsd -49.49 20.02 -2.473 0.013630 *
## male 130.46 32.28 4.042 0.0000583585 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 13.2 17.89 2.727 0.000156 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.151 Deviance explained = 18.9%
## -REML = 5947.4 Scale est. = 2.0255e+05 n = 807library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4a.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)